A new phase-change RAM (PCRAM) model is proposed in this paper for multi-level-cell (MLC) applications. The proposed model has been verified to reproduce the electrical behaviors well in various partial states. Moreover, it has been shown that the programming transient behaviors with various quenching times could be estimated using the proposed model. The new unified PCRAM model which describes three different regions of PCRAM with only one equation has three times smaller discrepancy between the model and measurement than the previous piecewise linear model. For the continuity in PCRAM resistance, the new model shows smooth transition at the boundaries between different regions, whereas some abrupt changes in PCRAM resistance were found in the piecewise model. The compactness with the simple parameter extraction, the continuity for the reliable simulation and the accuracy in the negative differential resistance region make the proposed model useful and suitable in developing the future MLC PCRAM circuits.