An alternating explicit-implicit domain decomposition method is proposed for the numerical solution of parabolic initial-boundary-value problems on parallel computers, which uses the alternating direction implicit-type operator splitting technique, where the operator splitting is domain decomposition based. This method satisfies a stability condition that imposes no additional restriction to the time step restriction imposed by the consistency condition, which guarantees a convergence of order \(O(\Delta t h^{-1}\sqrt{N_B/N}) + O(h^2)\) in an \(H^1\)-type norm, where \(N_B\) and \(N\) respectively denote the number of grid points on the interface boundaries \(B\) and the number of grid points on the entire discrete domain. Some numerical experiments are carried out to validate the theoretical results.