We study the dynamics of the leaky integrator recurrent neural network. Our results show that there exists at least one equilibrium point of the system, and the set of solutions of the leaky integrator recurrent neural dynamics is positive invariant and attractive. The globally exponential stabil- ity property of the system has been discussed. Our examples show that the leaky integrator recurrent neural network together with the state space search algorithm can be an effectively tool for many applications including data com- pression and learning the short-term foreign exchange rates.