Abstract: The prompt neutron decay constant α describes the temporal asymptotic behavior of neutron multiplying systems, and is critical in studying the kinetics properties of deep subcritical systems and accurately measuring their reactivity. Meanwhile, the α can be obtained by calculation and measurement, which makes it one of the bridges connecting reactor physics computation and experiments. Therefore, the accurate and stable solution of the α is of great significance for studying the kinetics characteristics in advanced nuclear energy systems such as accelerator driven sub-critical system (ADS), as well as the accurate measurement of reactivity in deep subcritical systems. However, the commonly used k-α iteration method cannot calculate the α in systems far from criticality due to the abnormal production of neutrons caused by the additive time-absorption cross section α/v. As the subcriticality increases, this numerical difficulty becomes more pronounced, thereby restricting the applicability of the commonly used approaches for systems over a wide range of subcritical states. This study aims to develop a continuous energy Monte Carlo code based on the α iteration method to accurately calculate the α of systems that covering a wide range of subcriticality including deep subcriticality. Based on the open source code OpenMC, the α iteration code OpenMC-Aiter was established. Firstly, the time source was used to replace the fission source for iteration, in which the complete fission chain was simulated within a single generation, and the contributions from neutron collisions were accumulated into the time source for the next neutron generation. To ensure calculation stability during the iteration process, the number of time source neutrons for the next generation was controlled. Finally, upon achieving source convergence through iteration, the α of the system could be obtained by the estimator. The code was validated by the Godiva, Pb-Bi-zoned and thorium-loaded KUCA experimental benchmarks. Results demonstrate that OpenMC-Aiter is capable of performing accurate and stable calculations for a series of systems spanning from critical to deep subcritical states, with the relative error between the calculated α eigenvalues and experimental values being less than 10%. Even in an extremely deep subcritical state of the thorium fuel KUCA with a k_eff of 0.006 26, OpenMC-Aiter can still calculate the α effectively. Compared with the improved k-α iteration method, OpenMC-Aiter with the α iteration method exhibits excellent applicability to problems involving a wide subcriticality range, and can serve as a powerful tool for the study of kinetics characteristics of advanced nuclear energy systems such as ADS and the accurate measurement of reactivity for deep subcritical systems.