Summary: We study two projection algorithms for solving the variational inequality problem in Hilbert space. The first algorithm is based on the inertial method, Tseng’s extragradient method and the shrinking projection method to obtain the strong convergence theorem without needing the sequentially weakly continuity of the variational inequality mapping. In the second algorithm, we use the Armijo-like step size rule so that it does not require the Lipschitz continuous condition of the associated mapping. Our results extend and improve some related results in the literature. Finally, the numerical examples are provided to illustrate the efficiency of our algorithms.