Proton　exchange　membrane　fuel　cell　(PEMFC),　according　to　its　merits　of　high　energy　density,　zero　emission,　and　low　noise,　has　been　widely　applied　in　industrial　appliances.　A　full　bridge　converter　is　used　to　implement　PEMFC-powered　DC　motor　bidirectional　rotation　in　this　paper.　For　the　sake　of　the　regulations　of　DC　motor　angular　velocity　as　well　as　bus　voltage,　an　adaptive　backstepping　sliding-mode　control　(ABSMC)　technique　integrated　with　Chebyshev　neural　network　(CNN)　is　proposed.　Based　on　the　equivalent-circuit　method,　the　control-oriented　model　of　the　PEMFC-powered　motor　system　is　structured.　By　constructing　Lyapunov　function,　the　adaptive　laws　and　control　laws　can　be　obtained　to　achieve　bus　voltage　and　angular　velocity　regulations　simultaneously.　Moreover,　the　proposed　neural　network　is　applied　to　estimate　the　uncertainties　of　the　system　through　orthogonal　basis　Chebyshev　polynomials.　To　highlight　the　advantages　of　proposed　technique,　a　proportional-integral　(PI)　control　was　introduced　subsequently　and　two　controllers　were　compared　via　numerical　simulations.　The　simulation　results　demonstrate　that　CNN　estimation　method　in　conjunction　with　backstepping　sliding-mode　shows　fast　and　accurate　response　even　though　the　existence　of　system　uncertainties　and　external　disturbances.　©　2020　Hydrogen　Energy　Publications　LLC