This paper develops a new family of models of generalized autoregressive heteroskedasticity (GARCH). The family captures the asymmetry in volatility based on a non-parametric method, namely spline method. Specifically, this paper proposes cubic and quadratic Spline-GARCH models. These models extend the partially non-parametric (PNP) GARCH model of Engle and Ng (1993) , which is based on piecewise linear functions. This paper also introduces cubic and quadratic Spline-EGARCH models which are generalized versions of Nelson(1991)'s exponential GARCH model. Due to the non-parametric nature of the proposed models, they are free from mis-specification problems which most of existing parametric models may suffer from. Using daily KOSPI return data for the period from January 1990 to June 2000, we find that the proposed models perform better in terms of likelihood values than other existing models including PNP GARCH model and Hentschel (1995) 's model, and that the quadratic Spline GARCH model , among proposed models, is the most parsimonious in capturing the asymmetric volatility in the data. The empirical examinations of the news impact curve also reveal that the existing parametric models over-estimate the volatility generated from extreme shocks and that they fail to incorporate so-called 'threshold effect' of a large positive shock. Further empirical investigation of the new models in risk management and out-of sample performance would be of considerable interest.