We study exciton states in a coupled double quantum well (CDQW) semiconductor structure. Exciton levels and binding energies of direct and indirect excitons are calculated for a symmetric CDQW system with an applied electric field. The exciton states are obtained by solving the exciton effective-mass equation in the momentum space using the modified Gaussian quadrature method. Within this approach we perform realistic calculations of the exciton states by taking into account the coupling between different subband pairs and calculate optical-absorption coefficients. The calculated values of the exciton binding energy are in a good agreement with the experiment and the calculated absorption spectra qualitatively agree with the measured photoluminescence excitation spectra.