The dielectric response of an electron system composed of an array of parallel quantum wires with weak coupling and strong coupling are studied, and the dispersions of the collective excitations and the single particle excitations (SPE) as functions of wave-vectors are given. It is found that for the nearly isolated quantum wires with several subbands occupation, there are a series of intra-subband collective excitations between corresponding intra-subband SPE spectra. There also exist inter-subband collective excitations when q(x) not equal 0 (q(x) is the wave-vector component in the modulation direction), whose energies are close by the corresponding inter-subband SPE spectra. The energy of the intra-subband mode decreases and that of inter-subband mode increases with q(x) increasing. The collective excitation dispersions show obvious anisotropy in the 1D quantum limit. The calculated results agree with the experiment well. The coupling between quantum wires affects markedly both the collective and single-particle excitations spectra. The system changes to a near-two-dimensional electron system gradually with increasing coupling.