A seventh order second derivative method with optimized hybrid points is proposed for the solution of first-order ordinary differential equations. The techniques of interpolation and collocation are employed for the construction of the method using a three-parameter representation of the hybrid points. By optimizing the local truncation error of the main method, the hybrid points are obtained and then used to derive second derivative method. The discrete schemes are produced as by-products of the continuous scheme and used to simultaneously solve initial value problems (IVPs) in block mode. The resulting schemes are self-starting, consistent, zero-stable, and A-Stable. The accuracy of the method was established using four test problems. The numerical results revealed that the new method performed better than existing methods in the cited literature.