In this paper, we developed a new continuous block method using the approach of collocation of the differential system and interpolation of the power series approximate solution. A constant step length within a half step interval of integration was adopted. We evaluated at grid and off grid points to get a continuous linear multistep method. The continuous linear multistep method is solved for the independent solution to yield a continuous block method which is evaluated at selected points to yield a discrete block method. The basic properties of the block method were investigated and found to be consistent and zero stable hence convergent. The new method was tested on real life problems namely: SIR model, Growth model and Mixture Model. The results were found to compete favorably with the existing methods in terms of accuracy and error bound.