For the quasi-two-dimensional disordered systems of the form of Nt×Nl, only considering the nearest-neighbor hopping integrals and using a special method to code the sites, we write the Hamiltonians of the systems as precisely symmetric matrixes, which can be transformed into three diagonally symmetric matrixes by the Householder transformation. The densities of states, the localization lengths and the conductance of the systems are calculated numerically using the negative eigenvalue theory and the transfer matrix method. We study mainly the quasi-two-dimensional disordered systems with four and five parallel chains. By comparing the results with that of the disordered systems with one chain, two chains and three chains, we find that the energy band of the system extends slightly and the distribution of the density of states changes obviously with the increase of the effective dimensionality. Especially, for the systems with four or five chains, at the energy band center, there exist extended states whose localization lengths are larger than the size of the systems, accordingly, they have greater conductance. With the increasing of the number of the chains, the correlated ranges expand and the systems present the behaviour similar to that with off-diagonal long-range correlation.