Natural, continuous tone images have a very important property of high correlation of adjacent pixels. Images which we wish to compress are usually non-stationary and can be reasonably modeled as smooth and textured areas separated by edges. This property has been successfully exploited in LOCO-I and CALIC by applying gradient based predictive coding as a major de-correlation tool. However, they only examine the horizontal and vertical gradients, and assume the local edge can only occur in these two directions. Their over-simplified assumptions hurt the robustness of the prediction in higher complex areas. In this paper, we propose an accurate gradient selective prediction (AGSP) algorithm which is designed to perform robustly around any type of image texture. Our method measures local texture information by comparison and selection of normalized scalar representation of the gradients in four directions. An adaptive predictor is formed based on the local gradient information and immediate causal pixels. Local texture properties are also exploited in the context modeling of the prediction error. The results we obtained on a test set of several standard images are encouraging. On the average, our method achieves a compression ratio significantly better than CALIC without noticeably increasing of computational complexity.