In this paper, we present a kernelized dictionary learning framework for carrying out regression to model signals having a complex non-linear nature. A joint optimization is carried out where the regression weights are learnt together with the dictionary and coefficients. Relevant formulation and dictionary building steps are provided. To demonstrate the effectiveness of the proposed technique, elaborate experimental results using different real-life datasets are presented. The results show that non-linear dictionary is more accurate for data modeling and provides significant improvement in estimation accuracy over the other popular traditional techniques especially when the data is highly non-linear.