The block cyclic projection method in the compressed sensing framework (BCPCS) was introduced for image reconstruction in computed tomography and its convergence had been proven in the case of unity relaxation (λ=1). In this paper, we prove its convergence with underrelaxation parameters λ∈(0,1). As a result, the convergence of compressed sensing based block component averaging algorithm (BCAVCS) and block diagonally-relaxed orthogonal projection algorithm (BDROPCS) with underrelaxation parameters under a certain condition are derived. Experiments are given to illustrate the convergence behavior of these algorithms with selected parameters.