The numerical solution of point kinetic equation with a group of delayed neutrons is useful in predicting neutron density variation during the operation of a nuclear reactor. The continuous indication of the neutron density and its rate of change is important for the safe start-up and operation of reactors. The Haar wavelet operational method (HWOM) has been proposed to obtain the numerical approximate solution of the neutron point kinetic equation that appears in a nuclear reactor with time-dependent and -independent reactivity functions. The present method has been applied to solve stiff point kinetic equations elegantly with step, ramp, zig-zag, sinusoidal, and pulse reactivity insertions. This numerical method has turned out as an accurate computational technique for many applications. In the dynamical system of a nuclear reactor, the point kinetic equations are the coupled linear differential equations for neutron density and delayed neutron precursor concentrations. These equations, which express the time dependence of the neutron population and the decay of the delayed neutron precursors within a reactor, are first order and linear, and essentially describe the change in neutron population within the reactor due to a change in reactivity. As reactivity is directly related to the control of the reactor, it is the important property in a nuclear reactor. For the purpose of safety analysis and transient behavior of the reactor, the neutron population and the delayed neutron precursor concentration are important parameters to be studied. An important property of the kinetic equations is the stiffness of the system. The stiffness is a severe problem in numerical solutions of the point kinetic equations, and it necessarily requires the need for small time steps in a computational scheme.