We developed a compact model for program transient simulation of 3-D charge-trap NAND flash on a bitline (BL) string level. By implanting the trapped charge parameters and the solutions obtained from modified 1-D Poisson equation into our unit cell model, we suggest that our model shows better accuracy compared to the existing model. After fitting the measured incremental step pulse programming (ISPP) data with the best accuracy, we investigated our model dependence on parameters relevant to electron tunneling/capture/emission and channel scaling. Also, the simulation results from various pulse conditions are investigated. Finally, program-inhibit characteristics by isolated channel were simulated and analyzed. Thus, we propose a widely available, highly accurate, and physics-based compact model for program operation of 3-D charge-trap NAND flash memories.