In this paper, we describe weak Galerkin finite element methods for solving hyperbolic problems on polygonal meshes. We propose both semidiscrete and fully discrete schemes to numerically solve the second-order linear wave equation. For the time discretization, we have used implicit second order Newmark scheme. For sufficiently smooth solutions, optimal order error estimate in the L 2 norm is shown to hold as O (h k+ 1+ τ 2), where h is the mesh size and τ the time step. An extensive set of numerical experiments are conducted to demonstrate the robustness, reliability, flexibility, and accuracy of the proposed method.