We consider the existence and stability of single-bump and multi-bump solutions of an Amari model, a class of integral-differential equations modeling a single layer of homogeneous neural network with both excitatory and inhibitory neuron. Existence results are obtained by combining several shifts of a one-bump solution. Dynamical properties are obtained by considering the equation as an infinite dimensional dynamical systems and the spectrum of single-bump and multi-bump solutions in terms of the coupling functions. The center manifold theory and its foliation are used to show exponential stability with asymptotic phase for multi-bump solutions. Numerical results for some possible bifurcation phenomena are also presented. Finally, we give a sufficient condition such that a 2-bump solution exists while the coupling function satisfying some particular conditions.