This research was published (in Chinese) in Chin. J. Nucl. Phys., 3, 2, 149 (1981). The average number of prompt neutron and the distributions of prompt neutron number probability P(ν) for spontaneous fission of 240Pu, 242Cm, and 244Cm relative to (252Cf) have been measured using a large gadolinium-loaded liquid scintillation counter with a co-incidence method. The results were (240Pu) = 2.141 ± 0.016, (242Cm) = 2.562 ± 0.020, and (244Cm) = 2.721 ±0.021. The measured distributions of prompt neutron number were fitted with Gaussian curves by a weighted least-squares method. The widths of Gaussian distribution are 1.149 ± 0.047, 1.159 ± 0.074, and 1.175 ± 0.098 for 240Pu, 242Cm, and 244Cm, respectively. These results as well as a previous measurement of spontaneous fission of 252Cf show the linear variation of σ with at the first order of approximation. The data were fitted by a least-squares method, and the result is given by σ = 0.980 + 0.076. This fact demonstrates the trend that the width of the excitation energy distribution of fission fragments increases with the average excitation energy of the fission fragments in the range of nuclides mentioned above.