This paper presents Singly Diagonally Implicit Runge-Kutta method based on cubic-spline Interpolation for the numerical solution of delay differential equation.The advantage of implicit Runge-Kutta methods is in their superior stability compared with the explicit methods, more so when applied to food limited equations.Our objective is to develop a scheme for solving Delay Differential equation usingsingly diagonally implicit Runge-Kutta method of 4^th order and 5^th order with the food limited population model equation and discussed about stability region. Errors of numerical results are compared with exact solution. This study is implemented with matlab programming.