A new scheduling to reduce the complexity of a turbo equalizer (TE) combined with a low-density parity-check (LDPC) decoder is proposed. Simple metrics and criteria for the proposed scheduling are derived from its convergence behavior. The TE with the proposed scheduling monitors the status of its iterative process and determines whether additional equalization is needed or not. Based on the decision, it adjusts performing equalization and reduces the execution number of equalization. Consequently, this leads to lowering the overall complexity of the TE. Numerical results show that the proposed scheduling has lower complexity than conventional schedulings, while they have almost the same performance.