Revealing the long-range elastic interaction and short-range core reaction between intersecting dislocations is crucial to the understanding of dislocation-based strain hardening mechanisms in crystalline solids. Phase field model has shown great potential in modeling dislocation dynamics by both employing the continuum microelasticity theory to describe the elastic interactions and incorporating the γ-surface into the crystalline energy to enable the core reactions. Since the crystalline energy is approximately formulated by linear superposition of interplanar potential of each slip plane in the previous phase field model, it does not fully account for the reactions between dislocations gliding in intersecting slip planes. In this study, an improved phase field model of dislocation intersections is proposed through updating the crystalline energy by coupling the potential of two intersecting planes, and then applied to study the collinear interaction followed by comparison with the previous simulation result using discrete dislocation dynamics. Collinear annihilation captured only in the improved phase field model is found to strongly affect the junction formation and plastic flow in multislip systems. The results indicate that the improvement is essential for phase field model of dislocation intersections.