AbstractThe multiplicity of the second‐largest eigenvalue of the adjacency matrix of a connected graph , denoted by , is the number of times of the second‐largest eigenvalue of appears. In 2019, Jiang, Tidor, Yao, Zhang, and Zhao gave an upper bound on for graphs with bounded degrees, and applied it to solve a longstanding problem on equiangular lines. In this paper, we show that if is a 3‐connected planar graph or 2‐connected outerplanar graph, then , where is the minimum degree of . We further prove that if is a connected planar graph, then ; if is a connected outerplanar graph, then , where is the maximum degree of . Moreover, these two upper bounds for connected planar graphs and outerplanar graphs, respectively, are best possible.