When the immersed boundary-lattice Boltzmann (IB-LB) model with the direct-forcing scheme is used to analyze the viscous fluid dynamics of the flow around a moving boundary, the interaction interface and the boundary force format directly affect the numerical accuracy and computational efficiency of the flow solver. Based on the implicit diffuse interface, an improved IB-LB model with the direct-forcing scheme was presented. The boundary force expression is derived based on Eulerian/Lagrangian variable identities. The interaction interface described by the transfer matrix couples the asynchronous movement between Lagrangian points. Use Richardson iteration to numerically solve the linear equations related to the boundary force and the non-slip velocity constraint. It not only overcomes the calculation efficiency problem caused by matrix inversion in the traditional velocity correction scheme, but also gets rid of the dependence of algorithm stability and Lagrangian point distribution. According to the Taylor-Green flow with analytical solution, the numerical accuracy of the present model is evaluated. The results show that the improved IB model can retain the second-order numerical accuracy of the background LB model. The numerical results of the flow over a stationary cylinder and an oscillating cylinder show that the model can provide reliable numerical predictions in the flow simulation involving complex geometries and moving interfaces. The IB-LB model yielded the force identity can effectively suppress the non-physical oscillation of the predicted hydrodynamic forces. The simulation of the flow around the undulating airfoil verifies the practicability of the current model, and can be further popularized in the fluid-structure coupling simulation of large-deformation flexible bodies.