The linear combination method is proposed to reduce the higher order mode (HOM) effect on the measurement of the prompt neutron decay constant using the α-fitting method. Conventional α-fitting utilizes the pulsed neutron source and estimates the prompt neutron decay constant by fitting the neutron counts at a single detector after pulse injection with a single exponential function. The proposed method reduces the spatial HOM effect with linear combination of the neutron counts at multiple detectors. For verification, we applied the conventional method and the proposed method to the analytical solution of the diffusion theory and the Monte Carlo simulation to estimate the prompt neutron decay constant of a one-dimensional infinite slab. Comparison of these results indicates that the proposed method enables estimation with the reduced HOM effect as opposed to the conventional method. Through the verification, we confirmed that the proposed method can be a candidate for a measurement method of the prompt neutron decay constant.