Block correlated coupled cluster theory with the complete-active-space self-consistent-field reference function (CAS-BCCC) is generalized for low-lying electronic excited states. By truncating the cluster operator up to the four-block correlation level, the corresponding CAS-BCCC4 method for excited states has been efficiently implemented. The approach is applied to study the excited-state potential energy surfaces for HF and C(2) and to evaluate adiabatic or vertical excitation energies for CH(2), N(2), and trans-1,3-butadiene. The results are compared with those from the full configuration interaction, the internally contracted multireference configuration interaction with singles and doubles, the complete active space with second-order perturbation theory, and other theoretical methods (if available). The CAS-BCCC4 approach is found to provide high accuracy calculations for the low-lying excited states of the systems under study.