The Kundu equation, which can be used to describe many phenomena in physics and mechanics, has crucial theoretical meaning and research value. In previous studies, the single Kundu equation has been investigated by the Riemann‐Hilbert method, but few researchers have focused on the coupled Kundu equations. To our knowledge, many phenomena in nature can be only described by coupled equations, such as species competition and signal interactions. In this paper, we discuss N‐soliton solutions of the coupled Kundu equations according to the Riemann‐Hilbert method. Starting from the spectral problem, the coupled Kundu equations are generated, and the Riemann‐Hilbert problem is presented. When the jump matrix of the Riemann‐Hilbert problem is the identity matrix, the N‐soliton solutions of the coupled Kundu equations can be expressed explicitly.