The general formalism of the block-correlated coupled cluster (BCCC) method, an alternative multireference coupled cluster method for calculating the ground-state electronic structures of molecular systems, has been presented. The BCCC theory is constructed in terms of a complete set of many-electron states of individual blocks, assumed that the whole system could be partitioned into a set of blocks. The reference state in the BCCC is selected as a tensor product of the most important many-electron state of each system block. By truncating the cluster operator to a certain n-block correlation level, an approximate but size-extensive BCCC method, denoted as BCCCn, is defined. For reducing the computational effort but without much loss of accuracy, the reduced density matrix is introduced to generate an optimal subset of many-electron states for each block. I have implemented the BCCCn (n=2,3) methods within the S=1/2 Heisenberg Hamiltonian, and applied them to calculate the ground-state energies of one-dimensional spin chains and quasi-one-dimensional two-leg spin ladders. The calculated results show that with the appropriate partition of the studied systems the BCCC3 method can yield quite satisfactory ground-state energies for these spin systems. (C) 2004 American Institute of Physics.