ABSTRACT This paper presents a new iteration method for the numerical solution of pressure equations arising in petroleum reservoir engineering. It utilizes a newly developed preconditioner and generalized conjugate gradient acceleration with a new residual constraint procedure. The Alternating Interblock Direction (AID) preconditioner exploits a natural way of alternating sweeps in xyz-directions and is free from the dependence on the choice of the first internal direction which is common with other methods. The generalized conjugate gradient algorithm is ORTHOMIN. It is further accelerated by an alternating direction residual constraints (ADC) which could make the summation of the residuals be zero simultaneously in all three axes. The new method can be easily vectorized and parallelized. It can also be adapted to equations other than the pressure equation. Its speed and robustness are proved to be favorable to previously published methods by numerical experiments.