The transport properties of a graphene multiquantum well system are investigated numerically using transfer-matrix method. There are transmission gaps for electrons and holes in the transmission spectra at tilted incidence. In the transmission gaps, a few resonant tunneling peaks appear, defined as transmission windows, which are related with the bound states in the quantum wells. Unlike conventional semiconductor nanostructures, the location and the width of the transmission windows are sensitive not only to the quantum well width but also the incident angle. The number of the quantum wells determines the fine structure of the transmission windows. The anisotropic property is affected in the following way: the increase in well width makes the nonzero-transmission incident angle range decrease, and the interference effect is enhanced as the well number increases. Tiny oscillation of the conductance and fine structures in the middle energy range are due to the resonant tunneling induced by the multiquantum well structure. These oscillating features may be helpful in explaining the oscillatory characteristics in experiment.