In response to the problem of holes in traditional coprime planar array （CPA） structures when using difference coarray （DCA） for two-dimensional direction of arrival （DOA） estimation， this paper proposes a hole-free coprime planar array （HFCPA） structure. The array is obtained by extending hole-free coprime linear arrays along the x and y axes， and its DCA is a hole-free rectangular array. Furthermore， this paper presents the optimal HFCPA structure to maximize the available continuous degrees of freedom. Simulation results demonstrate the superiority of the proposed array structure over existing coprime planar array structures in terms of the number of continuous degrees of freedom， virtualization efficiency， and two-dimensional DOA estimation performance.