The aim of this paper is to use the nonparametric regression to predict the loss ratio of non-life insurance as a dependent variable, based on incurred claims and earned premiums as two explanatory variables. Secondary data adopted in this research consists of twelve year time series of incurred claims and earned premiums from 2007/2008 to 2018/2019. In this paper we used R Package to apply kernel smoothing and estimation of the smoothing parameter (bandwidth) using cross validation methods. Afterwards, we applied a local polynomial (constant and linear) and Locally Estimated Smoothing (LOESS) in order to predict loss ratio. The results from local polynomial and LOESS indicate that the predicted value of loss ratio has a slight increasing trend over the upcoming three years period. All analysis and calculations in this paper has been performed using the R package codes as open source software.