In this paper, we first propose two batch blind source separation and equalization algorithms based on support vector regression (SVR) for linear time-invariant multiple input multiple output (MIMO) systems. The proposed algorithms combine the conventional cost function of SVR with error functions of classical on-line algorithm for blind equalization: both error functions of constant modulus algorithm (CMA) and radius directed algorithm (RDA) are contained in the penalty term of SVR. To recover all sources simultaneously, the cross-correlations of equalizer outputs are included in the cost functions. Simulation experiments show that the proposed algorithms can recover all sources successfully and compensate channel distortion simultaneously. With the use of iterative re-weighted least square (IRWLS) solution of SVR, the proposed algorithms exhibit low computational complexity. Compared with traditional algorithms, the new algorithms only require fewer samples to achieve convergence and perform a lower residual interference. For multilevel signals, the single algorithms based on constant modulus property usually show a relatively high residual error, then we propose two dual-mode blind source separation and equalization schemes. Between them, the dual-mode scheme based on SVR merely requires fewer samples to achieve convergence and further reduces the residual interference.