<p>In this paper, an extended homoclinic test is conducted for a generalized Hirota–Satsuma coupled KdV equation, from which periodic solitary wave solutions are obtained for the equation. Moreover, the periodic solitary wave solutions are analyzed via parameter restrictions by showing their periodic and solitary wave features in terms of the projection curves, as well as singularities and analyticities. Specifically, for singular situations, the periodic solitary wave solutions go to infinity and blow up at the singular points. For analytic situations, the periodic solitary wave solutions are smooth and their amplitudes only reach to finite values. The qualitative results on the periodic solitary wave solutions provide the evidence of the complexity and the richness of the dynamical behaviors underlying the generalized Hirota–Satsuma coupled KdV equation, which is helpful to describe the nonlinear dynamics of water waves.</p>