Kernel density estimators technique has been successfully applied to efficient Bit Error Rate (BER) computation issue under a diversity of simulation frameworks. However, as contemporary and emerging digital communication systems are increasingly provided with advanced transceivers, it is questionable if the Symbol Error Rate (SER) can be anyway derived from the BER. This paper investigates for a direct way to efficiently compute the SER. Focusing on the ubiquitous multi-level Quadrature Amplitude Modulation (QAM) transmission schemes, a Gaussian kernel-based estimator is designed. Simulation of the 4-QAM transmission scheme under various channel models shows that the proposed estimator can achieve efficient estimations with a very high degree of accuracy and reliability.