Conventional Direction-Of-Arrival (DOA) estimation approaches suffer from low angular resolution or relying on a large number of snapshots. The sparsity-based SPICE can work with few snapshots and has high resolution and low sidelobe level, but it only applies to narrowband signals. To solve the above problems, a new FrFT-SPICE method was proposed to estimate the DOA of wideband chirp signals with high resolution based on a few snapshots. First, the wideband chirp signal was taken on the Fractional Fourier Transform (FrFT) under a specific order so that the chirp wave in time domain could be converted into sine wave with single frequency in FrFT domain. Then, the steering vector of the received signal was obtained in FrFT domain. Finally, SPICE algorithm was utilized with the obtained steering vector to estimate the DOA of the wideband chirp. In the simulation with the same scanning grid and same snapshots, the DOA resolution level of the proposed FrFT-SPICE method was better than that of the FrFT-MUSIC method which combines MUltiple SIgnal Classification (MUSIC) algorithm and FrFT algorithm; and compared to the SR-IAA which utilizes Spatial Resampling (SR) and IAA (Iterative Adaptive Approach), the proposed method had a better accuracy. The simulation results show that the proposed method can estimate the DOA of wideband chirp signals with high accuracy and resolution based on only a few snapshots.