<p>In this paper, we introduce a new proximal-type regularization algorithm with a simple bi-stepsize rule for solving split monotone variational inclusions. The bi-stepsize rule is aimed to avoid the Lipschitz assumption of cost operator, which is usually unknown or difficult to estimate in practice. The regularization is used to establish strong convergence theorems for split monotone variational inclusions in real Hilbert spaces. Additionally, we give some numerical examples and applications in image reconstruction to illustrate the performance and superiority of the new proposed algorithm.</p>