In this paper, the exterior solution for a spherically symmetric black hole surrounded by plasma is studied in detail. After deriving the fundamental governing equations, the analytic solutions under two approximate conditions, ${g_{tt}}{g_{rr}} = - 1$ and $p = 0$ , are investigated. Comparing the two results with the accurate numerical solution, we find that the former approximation offers superior accuracy. This provides a basis for studying the quasinormal modes of perturbations as well as the shadow and ring when the black hole is surrounded by plasma.