To calculate the probability density function of the response of a random acoustic field, a change-of-variable perturbation stochastic finite element method (CVPSFEM), which integrates the perturbation stochastic finite element method (PSFEM) and the change-of-variable technique in a unified form, is proposed. In the proposed method, the response of a random acoustic field is approximated as a linear function of the random variables based on a first order stochastic perturbation analysis. According to the linear relationship between the response and the random variables, the formal expression of the probability density function of the response of a random acoustic field is obtained by the change-of-variable technique. The numerical examples on a two-dimensional (2D) acoustic tube and a three-dimensional (3D) acoustic cavity of an automobile cabin verify the accuracy and efficiency of the proposed method. Hence, the proposed method can be considered as an effective method to quantify the effects of the parametric randomness of a random acoustic field on the sound pressure response.