A mixed-basis method is developed for the calculation of the electronic structure of solids. The method is shown to be capable of treating crystals with large complex unit cells. A combined set of plane waves and Bloch sums of localized functions is employed as basis functions, thus leading to a very efficient representation of systems which contain both highly localized (atomiclike) and delocalized (plane-wave-like) electrons. The crystalline potential is determined in a fully self-consistent manner with no approximations made to its shape. The present method has the flexibility of being easily applicable to the study of many different systems (eg, surface calculations with supercells). Specific application is made to bulk Nb and Pd to demonstrate the efficiency and accuracy of the method. Very good agreement with experimental results and with band structures calculated using other methods is obtained. It is found that, with a mixed basis, only a relatively small set of functions is needed to obtain convergent wave functions for the electrons.