In synthetic aperture radar automatic target recognition (SAR-ATR), target information is usually propagated and reserved in complex-valued form, namely magnitude information and phase information. However, most of the existing SAR target recognition methods only focus on real-valued (magnitude information) calculations and ignore the phase information of targets, yielding poor recognition performance. To overcome this limitation, this paper proposes a multi-stream feature fusion SAR target recognition method based on complex-valued operations, called MS-CVNets, to utilize the phase information of the target effectively. First of all, a series of complex-valued operation blocks are constructed to satisfy the network training in the complex field, such as complex convolution, complex batch normalization, complex activation, complex pooling, complex full connection, etc. Besides, a multi-stream structure is employed by applying different convolution kernels to extract multi-scale information of targets, further enhancing the representation ability of the model. Experimental results on the MSTAR dataset illustrate that, compared with current state-of-the-art real-valued based models, MS-CVNets can achieve better recognition results under both standard operating conditions (SOC) and extended operating conditions (EOC), validating the effectiveness and superiority of the proposed method.