A detection algorithm based on support vector machine (SVM) is proposed for four-level pulse amplitude modulation (PAM-4) signals in free-space laser communication. Using the power spectral density inversion method, we simulate the atmospheric phase screen. Under the assumption of Taylor frozen flow, we obtain the optical field signal of the laser carrier propagating through the atmospheric turbulent channel. After Gaussian white noises to the signal are added at the receiving end, the PAM-4 signal is judged by the SVM detection algorithm. SVM detection algorithm is independent on the atmospheric channel. Firstly, SVM detection algorithm groups the received signal data, trains the learning and adjusts the parameters through cross validation of each packet data. Secondly, the optimal hyper-planes between every two adjacent levels can be determined by the cascaded two-level classifications. Lastly, the signal judgment can be made by SVM. The bit error rate (BER) obtained by SVM detection algorithm is better than that of the double-step blind detection, which is comparable to that of the optimal bound detection for weak atmospheric turbulences. It is shown that the SVM detection algorithm has a good performance.