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 FEL radiation generation. In this paper, 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 SASE and seeded extreme ultraviolet and soft x-ray FELs based on laser plasma accelerators. Show Partial Abstract