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The generalized l₁ greedy algorithm was recently proposed and shown to outperform the standard reweighted l₁-minimization and l₁-greedy algorithms for image reconstruction in computed tomography (CT). Herein, this algorithm is extended as a semisoft generalized l₁ greedy algorithm by adapting the wavelet technique of semisoft thresholding. The extended algorithm can also be applied to image reconstruction by incorporating it into the BCPCS framework, resulting in a semisoft generalized total variation minimization (SSGTV) algorithm for CT. Numerical tests indicate that the proposed SSGTV algorithm improves the image reconstruction for CT.