Machine learning methods, such as decision trees and deep neural networks, are becoming increasingly important and useful for data analysis in various scientific fields including dynamics and control, signal processing, pattern recognition, fluid mechanics, and chemical synthesis, etc. For future engine design and performance optimization, there is an urgent need for a robust predictive model which could capture the major combustion properties such as autoignition and flame propagation of multicomponent fuels under a wide range of engine operating conditions, without massive experimental measurement or computational efforts. It will be shown that these long-held limitations and challenges related to complex fuel combustion and engine research could be readily solved by implementing machine learning methods. In this paper, both random forest and deep neural network algorithms were implemented to predict ignition delay times, flame speeds, octane ratings, and CA50 values (crank angle corresponding to 50% of the heat release rate) in homogenous charge compression ignition (HCCI) engines for multicomponent gasoline surrogates. Various training models were first tested to optimize CPU efficiency while maximizing accuracy and reducing error, and then different machine learning models were tested on their ability to predict outputs based on conditions not included in the training set. Although differences in random forest and deep neural networks are noted in the training-prediction process, it is found that both random forests and deep neural networks exhibit good ability to predict results accurately with small training effort, by comparing with data extracted from simulations and previous models. For flame propagation, both methods predict flame speed values more accurately than a proposed empirical model in the literature. We have therefore demonstrated the usefulness and great potential of these machine learning methods to assist engine combustion prediction and control.