Capillary pressure is one of the most important parameters affecting fluids distribution in a reservoir rock and is an essential input parameter for reservoir simulation. Measurement of capillary pressure data, in the context of special core analysis (SCAL) is a time and cost consuming process that does not often lead to accurate and reliable results. Routine core analysis (RCAL) data, on the other hand, can be obtained by simple, accurate, and cost-effective procedures. In this paper, the idea of using RCAL measurements to predict SCAL data (more specifically capillary pressure data) using Artificial Neural Network (ANN) approach is presented. An ANN with Multi-Linear Perceptron structure and feed-forward propagation was used to predict capillary pressure curves for a target reservoir under study. The ANN model was then optimized by Cuckoo optimization algorithm (COA). The ANN-COA model was used for 30 measurements, composed of both drainage and imbibition data points obtained from 15 core samples using centrifugation method. Out of this databank, 16 measurements were used for training and the remaining 14 measurements were used as the testing dataset. It was obtained that the optimized model shows a profound predicting performance based on the excellent value of coefficient of determination for predicted versus measured capillary pressure data.