As a popular meshfree particle method, the smoothed particle hydrodynamics (SPH) has suffered from not being able to directly implement the solid boundary conditions. This influences the SPH approximation accuracy and hinders its further development and application to engineering and scientific problems. In this paper, a coupled dynamic solid boundary treatment (SBT) algorithm has been proposed, after investigating the features of existing SPH SBT algorithms. The novelty of the coupled dynamic SBT algorithm includes a new repulsive force between approaching fluid and solid particles, and a new numerical approximation scheme for estimating field functions of virtual solid particles. The new SBT algorithm has been examined with three numerical examples including a typical dam-break flow, a dam-break flow with a sharp-edged obstacle, and a water entry problem. It is demonstrated that SPH with this coupled dynamic boundary algorithm can lead to accurate results with smooth pressure field, and that the new SBT algorithm is also suitable for complex and even moving solid boundaries.