In this work, compressive strength of lightweight geopolymers produced by fine fly ash and rice husk–bark ash together with palm oil clinker (POC) aggregates has been investigated experimentally and modeled based on artificial neural networks. Different specimens made from a mixture of fine fly ash and rice husk–bark ash with and without POC were subjected to compressive strength tests at 2, 7, and 28 days of curing. A model based on artificial neural networks for predicting the compressive strength of the specimens has been presented. To build the model, training and testing using experimental results from 144 specimens were conducted. The data used in the multilayer feed-forward neural networks models are arranged in a format of six input parameters that cover the quantity of fine POC particles, the quantity of coarse POC particles, the quantity of FA + RHBA mixture, the ratio of alkali activator to ashes mixture, the age of curing and the test trial number. According to these input parameters, in the neural networks model, the compressive strength of each specimen was predicted. The training and testing results in the neural networks model have shown a strong potential for predicting the compressive strength of the geopolymer specimens in the considered range.