Abstract This paper is concerned with a solution of backward pseudo-Parabolic equation u t − α Δ u t + G ( ∥ ∇ u ∥ L 2 ( Ω ) ) ( − Δ ) β u = K ( t , x ) subject to the final data which is blurred by random Gaussian white noise. The primary aim of this work is to obtain the solution u . This problem is severely ill-posed (the solution’s behavior does not change continuously with the final condition). By using a statistical method, we estimate the value data from observation data and the Fourier truncation method is used to propose a regularized solution. Under some priori assumptions, we derive an error estimate between a mild solution and its regularized solution. Finally, a numerical example is given to illuminate the effect of our method.