The percent level energy spread and large divergence of laser-plasma beam are the main challenges of realizing compact short-wavelength free-electron lasers based on laser-plasma accelerators. These issues can be solved with proposed transverse gradient undulator method or bunch decompression method along with proper transport design. We present a study of using an expected 500 MeV laser-plasma beam with 0.3 m m⋅ m r a d normalized emittance and 0.3 m r a d divergence at Peking University to drive compact free-electron laser at 30 nm. We employ the bunch decompression method with a chromatic matching beamline as well as the transverse gradient undulator method with assumed matched beam. Simulation shows that 700 MW power, 9.7 fs pulse duration and 0.85% relative bandwidth FEL output can be obtained using chromatic matched bunch decompression method. FEL with similar performance can be obtained using the transverse gradient undulator scheme.