Natural gas hydrate has been widely of concern due to its great potential in application to address problems including gas storage, transmission, separation techniques, and also as energy resource. Accurate prediction of hydrate formation phase equilibrium conditions is essential for the optimized design during natural gas production, processing, and transportation. In this study, a novel graphical alternating conditional expectation (ACE) algorithm was proposed to predict hydrate formation phase equilibrium conditions for sweet and sour natural gases. The accuracy and performance of the presented ACE model were evaluated using 1055 data points (688, 249, and 118 data points for sweet natural gas, CO2-CH4, and H2S-CO2-CH4 systems, respectively) collected from literature. Meanwhile, a comparative study was conducted between the ACE model and commonly used correlations, including thirteen models for sweet natural gases, three models for CO2-CH4 binary system, and seven thermodynamic models for H2S-CO2-CH4 ternary system. The obtained results indicated that the proposed ACE model produces the best results in prediction of hydrate phase equilibrium temperature for sweet natural gases and pressure for CO2-CH4 system with average absolute relative deviation (AARD) of 0.134% and 2.75%, respectively. The proposed quick and explicit ACE model also provides a better performance in prediction of hydrate phase equilibrium pressure for H2S-CO2-CH4 ternary systems with AARD=5.20% compared with seven thermodynamic methods considered in this work, except for CPA/Electrolyte/Chen–Guo combined model (AARD=4.45%).