As technology develops, many people are exposed to radiation in hospitals and living spaces. It is widely known that radiation-related cancer risk increases as the background rate increase over time. Accurately quantifying the risk of exposure to radiation is a major study in radiation epidemiology. The solid cancer incidence data among Life Span Study (1958-2009) was used to estimate the risk associated with radiation by using Bayesian analysis. First, we considered the piecewise linear model, which estimates the slope by dividing the dose range, as dose-response function. In the piecewise linear model, the slope tends to change rapidly at the cut points. In this paper, we consider the Gaussian process with a covariance matrix to allow a dose difference structure to the dose category slopes. Finally we compare the results with other models using Bayesian analysis. As a result, estimated risk appeared slightly smaller than the Piecewise linear model with general assumption.