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Soft ground improvement is a considerable concern of many researchers worldwide in geotechnical works. In this study, the compressibility of clay (Cc) was considered for compacting the soil for soft ground improvement, and various novel intelligence models have predicted it. Indeed, a dataset containing 739 samples in the laboratory was investigated and used to develop intelligence models for predicting Cc. The extreme learning machine (ELM) was selected for this task. It was then optimized by six metaheuristic algorithms, including particle swarm optimization (PSO), moth search optimization (MSO), firefly optimization (FO), cuckoo search optimization (CSO), bees optimization (BO), and ant colony optimization (ACO), named as PSO-ELM, MSO-ELM, FO-ELM, CSO-ELM, BO-ELM, and ACO-ELM models. We used 517 samples (~ 70%) to develop models and 222 samples (~ 30%) to test the accuracy of those models. The results indicated that the accuracies of hybrid meta-heuristic-based ELM models improved from 3–5% compared to the original ELM model in predicting Cc. The highest accuracy of 87% was also reported in this study with the BO-ELM model when predicting Cc on the testing dataset. It was introduced as a robust model for predicting Cc in practical engineering that can assist in improving the soft ground.