This study proposes a method for generating acoustic noise sequences with different distributions and coloured spectra. The noise samples are obtained by passing a non-Gaussian white noise through a finite impulse response filter. The resulting power spectral density is proportional to 1/fβ, where β is a positive power-law exponent. The noise samples pattern is determined by the Kurtosis ratio. The proposed generator is evaluated by comparing real and artificial acoustic noises statistics in the time and frequency domains. The results show that the generated coloured sequences achieved the PSD decaying rate and also the non-Gaussian pattern of the real environmental acoustic noises.