In this paper, we establish a linear convergence result for the forward-backward splitting algorithm in the finding a zero of the sum of two maximal monotone operators, where one of them is set-valued strongly monotone and the other is Lipschitz continuous. We show that our convergence rate is better than Douglas–Rachford splitting algorithm’s rate used by Moursi–Vandenberghe (J Optim Theory Appl 183, 179–198, 2019) under the same assumptions in most of important subcases. In addition, the forward-backward splitting requires only one resolvent while it is necessary to compute the resolvents of both operators in Douglas–Rachford splitting, which means the forward-backward splitting is more preferable. We also compare the linear convergence rate of the forward-backward splitting to the rate of Douglas–Rachford splitting acquired by Giselsson (J Fixed Point Theory Appl 19, 2241–2270, 2017) when the Lipschitz continuity of the single-valued operator is strengthened with the cocoercivity.