Macroscopic link-based flow models are efficient for simulating flow propagation in urban road networks. Existing link-based flow models described traffic states of a link with two state variables of link inflow and outflow and assumed homogeneous traffic states within a whole link. Consequently, the turn-level queue length change within the link cannot be captured accurately, resulting in underrepresented queue spillback. Moreover, a constant link free-flow speed was assumed to formulate models, restricting their applicability in modeling phenomena involving time-varying free-flow speed. This study proposed a new link-based flow model by introducing an additional state variable of link queue inflow and adapting the link outflow to be free-flow speed-dependent. In our model, the vehicle propagation within each link is described by the link inflow, queue inflow, and outflow, which depends on the link free-flow speed changes and signal control. A node model is further defined to capture the presence of potential queue spillback, which estimates the constrained flow propagation between adjacent road segments. Simulation experiments were conducted on a single intersection and on networks to verify the proposed model performance. Results demonstrate the predictive power of the proposed model in simulating traffic proppagations for networks with multiple turning movements and time-varying free-flow speed. Our model outperforms the baseline link-based flow model while preserving the computational tractability property of link-based flow models.