This paper investigates spillover effects from the U.S. stock market to the Korean stock market by considering a functional regression model. Instead of using stock market indices, we consider cross-sectional distributions of all stock returns that comprise the KOSPI index and the S&P 500 index. We use daily data from January 2005 to December 2013 and consider three subsamples: pre-crisis, crisis and post-crisis period. We estimate a functional regression model and adopt novel econometric tools recently proposed by Hu et al. (2016) to analyze the relationship between cross-sectional distributions of two stock markets. We use response functions to examine how each moment and tail probability of the Korean stock market distribution react to shocks in the US stock market distribution. We also conduct variance decomposition and provide interpretations on spillover effect from the U.S. stock market to the Korean stock market. The spillover effects to mean, variance and left tail probability were higher in the post-crisis period than in the pre-crisis period and were the highest during the crisis period. On the contrary, the spillover effect to right tail probability was the highest in the post-crisis period.