In this paper，we study the valuation of credit derivatives with jumps in interest rates and propose a general pricing model under the linear-quadratic jump-diffusion framework．Jumps in interest rates would influence intensities of default times，which decide the default possibilities that determine the prices of credit derivatives．We let the components of linear-quadratic process be cross-exciting and facilitate the description of complex event dependence structures．To illustrate how our model works，we make an application on CDS under the specific underlying processes，and an explicit formula of the fair CDS spread can be obtained through a system of matrix Riccati equations．