Compact laser-plasma accelerators can produce high energy electron beams with low emittance, high peak current but a rather large energy spread. The large energy spread hinders the potential applications for coherent free-electron laser (FEL) radiation generation. We discuss a method to compensate the effects of beam energy spread by introducing a transverse field variation into the FEL undulator. Such a transverse gradient undulator together with a properly dispersed beam can greatly reduce the effects of electron energy spread and jitter on FEL performance. We present theoretical analysis and numerical simulations for self-amplified spontaneous emission and seeded extreme ultraviolet and soft x-ray FELs based on laser plasma accelerators.