The variational model inversion (VAR) method for synthetic aperture radar (SAR) wind retrieval based on the Bayesian theory can overcome the limitations of the traditional wind streak algorithm by introducing background wind and considering all sources of error, but its optimal solution is unstable and the time latency is long. In this article, we propose a new wind retrieval method by applying the optimal interpolation (OI) theory to construct a formula that considers the SAR information, background information coming from the numerical prediction model, and their associated well-characterized errors. The retrieved wind vector can be acquired by the analytic solution of the OI formula. The results from the simulation data show that the error of the OI-retrieved wind is smaller than that of background wind in all considered cases; in particular, the accuracy of the OI-retrieved wind speed is significantly improved. Experiments on the Sentinel-1 SAR data show that the root mean square error of the OI-retrieved wind speed and direction are 1.4 m/s and 35°, respectively. Compared with other methods, the retrieved wind speed accuracy of the OI method is similar to that of the VAR method but higher than that of the direct wind retrieval method. The time latency of the OI method is the shortest, and the calculation efficiency is much higher than that of the VAR method. The results indicate that the OI method can be effectively applied to SAR wind retrieval.