Below is the list of few Nigerian company that is currently accepting Industrial training application. This company is comprises of oil and non company.

Do well to check on them and equally apply if you meet the criteria.
1) 2018/2019 Switbai Graduate Internship Programme

Switbai is a web and mobile application development company. Founded in 2013, our products cut across educational apps, e-commerce, online learning, UX design and business strategy- all leveraging on human-computer interaction. Switrez, our flagship app, is used by about 3000 students, parents and teachers.
2) 2018 Saipem Contracting Nigeria Ltd Industrial Attatchment Application

Saipem, One of the global leader in drilling services, as well as in the engineering, procurement, construction and installation of pipelines and complex projects, onshore and offshore, in the oil & gas market is currently accepting Application from interested student for the 2018 Industrial Training Program.
3) ExxonMobil Internship Application

ExxonMobil is dedicated to an ongoing recruiting program and our geoscience internship is one avenue we pursue to find qualified candidates. Each year, ExxonMobil hires bright and energetic students who are participating in an undergraduate program in a higher institution. Internships are available year round.
4) MTN Nigeria 2018 Customer Service Accelerated Nationwide Internship Programme

MTN Nigeria – The leader in telecommunications in Nigeria, and a part of a diverse community in Africa and the Middle East, our brand is instantly recognisable. It is through our compelling brand that we are able to attract the right talents who we carefully nurture by continuously improving our employment offerings even beyond reward and recognition.

We are proudly Nigeria’s pioneer and largest Brewing firm. Our company was incorporated in 1946 and in June 1949, we recorded a landmark when the first bottle of STAR lager beer rolled off our Lagos Brewery bottling lines. This first brewery in Lagos has undergone several optimization processes and as at today boasts of one of the most modern brew house in the country. Nigerian Breweries Plc is a socially responsible corporate organization with a good track record of corporate social initiatives. Nigeria’s Breweries Student Industrial Training Programme offers Nigerian students in Higher Institutions the opportunity to gain work experience in different locations.
6) 2018 Schlumberger Internship Application For Graduates And Undergraduate

An Internship with Schlumberger offers a unique insight to see whether your career with them is right for you. Whether you are considering a field-based role, an internship in one of our research, engineering, manufacturing, and sustaining centers or an office-based geosciences, petrotechnical or business support role, you will be expected to make a real contribution to the company. Application link
7) 2018 Total Internship Application

Total Exploration and Production Nigeria limited, one of the leading International Oil company in Nigeria, in-line with its Training and Development Department (Deepwater, Port-Harcourt District and Corporate) have commenced the collection of Application for the March 2018- August 2018 batch of Industrial Trainees request.
Shell Student Industrial Training and Internship Programme

Shell Companies in Nigeria’s Student Industrial Training Programme offers Nigerian students in Higher Institutions the opportunity to gain work experience in different locations. The following are the list of eligible courses .

To start application, View source: http://9flux.com/current-2018-internships-you-should-not-miss/