© 2016, Springer Science+Business Media Dordrecht.We study the dynamics of optical solitons in negative-index materials with non-Kerr nonlinearity and third-order dispersion. Three types of non-Kerr law nonlinearities are considered. They are power law, parabolic law and dual-power law. With the help of the extended trial equation method, various families of solitons including bright, dark and singular solitons are derived. The presented results could provide a method and technique in ultra-short optical soliton control in various kinds of non-Kerr law nonlinear negative-index materials.