This paper deals with the problem of three-dimensional autoregressive (3-D AR) model order estimation. Especially, we develop a practical algorithm to estimate the 3-D AR order (P1,P2,P3) corresponding to the quarter-space (QS) region of support. The proposed method is derived from the minimum description length (MDL) criterion and uses the minimum eigenvalue of the covariance matrix of the underlying 3-D Gaussian process. Numerical simulations are presented to illustrate the performances of the new proposed algorithm and compare it with a recently developed method