Hidden Markov Model (HMM) based on symmetric lambda distribution framework is implemented for the study of return time-series in the financial market. Major features in the S&P500 index, such as regime identification, volatility clustering, and anti-correlation between return and volatility, can be extracted from HMM cleanly. Univariate symmetric lambda distribution is essentially a location-scale family of exponential power distribution. Such distribution is suitable for describing highly leptokurtic time series obtained from the financial market. It provides a theoretically solid foundation to explore such data where the normal distribution is not adequate. The HMM implementation follows closely the book: "Hidden Markov Models for Time Series", by Zucchini, MacDonald, Langrock (2016).