The searching for potential quantum chromodynamics (QCD) phase transition signals is a fundamental goal of on-going experiments on heavy-ion collisions, which is critical to understanding the properties of strongly interacting matter under extreme conditions, the inner structure of compact stars, gravitational waves emitted from neutron star mergers, etc. In particular, the beam energy scan program carried out at the Relativistic Heavy-Ion Collider (RHIC) provides a unique tool that enables studies into the QCD phase diagram and the conjectured QCD critical point. Besides the event-by-event fluctuation of conserved charges, which has been widely accepted as a useful study of the QCD critical point, the production of light nuclei can serve as a sensitive observable to the QCD phase transitions in high-energy heavy-ion collisions. The density fluctuation and correlation among nucleons are automatically encoded in the production of light nuclei in heavy-ion collisions. This study aims to demonstrate how to probe QCD phase transition with light nuclei production in heavy-ion collisions. The progress of studies in this area over the last few years is reviewed. The nucleon coalescence model provides a suitable tool for the study of the effects of density fluctuation/correlation on light nuclei production. A transport model based on the Nambu-Jona-Lasinio (NJL) model is developed to simulate the occurrence of the first-order chiral phase transition in heavy-ion collisions. Within the coalescence model for light nuclei production, the yield ratio NtNp/Nd2 of protons (p), deuterons(d), and tritons (t) is shown to be sensitive to the nucleon density fluctuation and correlation and can function as a good probe to the non-smooth QCD phase transition. The production of light nuclei in heavy-ion collisions encodes the information about baryon density fluctuations and correlations, and enhancements of the yield ratioNtNp/Nd2 could serve as an indicator for the occurrence of a first-order or second-order QCD phase transition.