A simple one-dimensional model is suggested to simulate some aspects of the dynamics of granular shear flows. The model consists of a viscoelastic packet bouncing between two harmonically oscillating walls. The amplitude and frequency of the wall motion are related to the concentration and shear rate respectively. The dynamics of the system is studied and it is shown that periodic as well as chaotic motions are possible for different parameters and initial conditions. Results are presented in the form of time histories, power spectral densities, phase diagrams, Poincaré maps and bifurcation diagrams. Some of the characteristics present in the two-dimensional granular shear flows are present in this simple model. It is promising that such analysis can provide better understanding of the transitional behavior of the constitutive relation between the rapid shear and the quasi-static flows.