When the compressive sensoring is used in wavefront measurement, classic methods of slopes’ restoration has a relatively low precision, which make it difficult to measure the atmospheric turbulence wavefront. In the paper, a deep neural network is presented to improve the slopes’ restoration precision. The traditional compressive sensing technology does not take into account the relatively small slopes, which increases the wavefront measurement errors. To measure the complex wavefront induced by atmospheric turbulence with a high speed, the paper presents an improved deep neural network to restore the slopes from sparse ones with high precision, which improves the precision of wavefront reconstruction. When the compression ratio is ranged from 0.1 to 0.9, the wavefront error PV (Peak to valley) of the compressed wavefront detection algorithm based on depth neural network (DNNCWS) proposed in this paper is better than 0.014 μm, and the running time of the algorithm is 4.4 ms. In the case of low signal-to-noise ratio, the residual wavefront PV is better than 0.011 μm. In addition, the simulation results indicate that it has good anti-noise performance. The DNNCWS improves the detection accuracy of compressive sensing and overcomes the problem of low accuracy for complex aberration induced by atmospheric turbulence. It can also be used in other adaptive optical applications, such as laser communication and retinal imaging.