An artificial neural network (ANN) is successfully presented for prediction acidity constant (pKa) of various benzoic acids and phenols with diverse chemical structures using a nonlinear quantitative structure-property relationship. A three-layered feed forward ANN with back-propagation of error was generated using six molecular descriptors appearing in the multi-parameter linear regression (MLR) model. The polarizability term $(pi_1)$, most positive charge of acidic hydrogen atom $(q^+)$, molecular weight (MW), most negative charge of the acidic oxygen atom $(q^-)$, the hydrogen-bond accepting ability $(epsilon_B)$ and partial charge weighted topological electronic (PCWTE) descriptors are inputs and its output is pKa. It was found that properly selected and trained neural network with 205 compounds could fairly represent dependence of the acidity constant on molecular descriptors. For evaluation of the predictive power of the generated ANN, an optimized network was applied for prediction pKa values of 37 compounds in the prediction set, which were not used in the optimization procedure. Squared correlation coefficient $(R^2)$ and root mean square error (RMSE) of 0.9147 and 0.9388 for prediction set by the MLR model should be compared with the values of 0.9939 and 0.2575 by the ANN model. These improvements are due to the fact that acidity constant of benzoic acids and phenols in water shows nonlinear correlations with the molecular descriptors.