The use of machine learning (ML) techniques to model quantitative composition-property relationships in concrete has received substantial attention in the past few years. This paper presents a novel hybrid ML model (RF-FFA) for prediction of compressive strength of concrete by combining the random forests (RF) model with the firefly algorithm (FFA). The firefly algorithm is utilized to determine optimum values of two hyper-parameters (i.e., number of trees and number of leaves per tree in the forest) of the RF model in relation to the nature and volume of the dataset. The RF-FFA model was trained to develop correlations between input variables and output of two different categories of datasets; such correlations were subsequently leveraged by the model to make predictions in previously untrained data domains. The first category included two separate datasets featuring highly nonlinear and periodic relationship between input variables and output, as given by trigonometric functions. The second category included two real-world datasets, composed of mixture design variables of concretes as inputs and their age-dependent compressive strengths as outputs. The prediction performance of the hybrid RF-FFA model was benchmarked against commonly used standalone ML models - support vector machine (SVM), multilayer perceptron artificial neural network (MLP-ANN), M5Prime model tree algorithm (M5P), and RF. The metrics used for evaluation of prediction accuracy included five different statistical parameters as well as a composite performance index (CPI). Results show that the hybrid RF-FFA model consistently outperforms the standalone ML models in terms of prediction accuracy - regardless of the nature and volume of datasets.