Summary: A new hybrid nonlinear numerical method is proposed for solving initial value problems in ordinary differential equations. The proposed hybrid method is found to be second order accurate and linearly stable. The stability region of the method is also presented in addition to the development of the local truncation error associated with the method. Some initial value problems of both scalar and vector valued type are tested to illustrate the efficiency of the method. In order to test the performance, absolute maximum error, absolute error at the last nodal point of the integration interval under consideration and CPU values have been calculated by the proposed method, first order linear explicit Euler's method, first order nonlinear explicit Fatunla's method and second order linear explicit Heun's method. The method is found to be more reliable than these standard existing methods available in literature having same order of accuracy or lower. MATLAB R2017a has been used for numerical computations and plotting of results produced by all the methods considered.