Environmental vibration is one of the non-periodic and random broadband excitations. It is of great significance to study the characteristics of vibration energy harvesters under environmental vibrations. In this paper， the modified stochastic averaging method is used to solve the following parameters of piezoelectric beam with a variable cross-section： steady-state probability densi? ty function of equivalent amplitude， displacement and velocity， joint probability density function of displacement， and velocity and steady-state mean square output voltage. Then the study investigates the energy acquisition efficiency of a piezoelectric beam with a variable cross-section under Gaussian white noise excitation. The results show that when the load resistance reaches a certain val? ue， the variable section piezoelectric beam with a section coefficient β>0 can produce better steady-state mean square output volt? age than the constant section piezoelectric beam with β=0； when the section coefficient β>0， with the increase of the reciprocal of the product of resistance and capacitance， the mean square voltage of the variable-section piezoelectric beam shows a gradually de? creasing trend. The trend shows the following rules： when the reciprocal value of the resistance and capacitance reaches a certain value， the larger the β value is， the higher the mean square voltage will become； with the increase of the noise intensity， the mean square voltage of the variable-section piezoelectric beams shows a trend of increasing gradually； when the noise intensity reaches a certain value， the larger the β value is， the higher the mean square voltage will become. The research results in this paper can pro? vide a theoretical basis for the design and application of the variable-section piezoelectric cantilever energy harvesting system.