People use multiple frames of reference (FORs) for representing and updating spatial relationships between objects in a complex environment. “Frame of Reference-based Map of Salience” theory (FORMS) suggests that FORs with high salience may be processed in priority. Here, we report a computational neural network model for a two-cannon task, which naturally involves multiple FORs with different levels of salience: intrinsic frame of reference (IFOR) and egocentric frame of reference (EFOR). The goal is to investigate the computational neural mechanisms underlying human spatial performance. Our simulation results fit earlier behavioral results well. The model suggests although multiple FORs may be initially represented independently, they interfere with each other by the inhibitory competition of neurons in the later process (in hidden layer) for conflict resolution. Moreover, salience may modulate the competition by prioritizing FORs with high salience levels. These results represent a connectionist support for the FORMS theory.