For a graph \(G\), Chartrand et al. defined the rainbow connection number \(rc(G)\) and the strong rainbow connection number \(src(G)\) in “G. Chartrand, G.L. John, K.A. McKeon, P. Zhang, Rainbow connection in graphs, Mathematica Bohemica, \(133(1)(2008) 85-98\)”. They raised the following conjecture: for two given positive integers \(a\) and \(b\), there exists a connected graph \(G\) such that \(rc(G) = a\) and \(src(G) = b\) if and only if \(a = b \in \{1,2\}\) or \(3 \leq a \leq b”\). In this short note, we will show that the conjecture is true.