An implicit finite volume method (FVM) with Newmark scheme is proposed for the sound propagation problem, and it is used to simulate the propagation of the plane wave. By comparing to the results from the FVM with that of explicit central difference algorithm, the numerical error, stability and computational consumption are analyzed. It is shown that both methods can acquire accurate numerical solutions when λ／Δx≥10. The relative peak error of the implicit scheme is less than 1％ when ω₀Δt≤0.3. With the same time step and spatial step, the numerical result of the implicit scheme agrees better with the exact result. The implicit method treats the absorbing boundary condition more accurate than the explicit method, but it is reverse for the total reflecting boundary condition. The two methods consume similar memory and the explicit method consumes less CPU time.