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Based on the recent experimental measurement results of fluid particle transverse accelerations in fully developed pipe turbulence published in Nature (2001) by Porta et al [1], this study develops a multiscale statistical model which considers both normal diffusion in molecular scale and anomalous diffusion in vortex-scale.And a new acceleration probability density function, called Power-Stretched Gaussian Distribution model (PSGD), is then presented, which is stated as p(x)=C/(x+x0)2*1/√2πσ2/3 exp(-(x+x0)2/3/2σ2/3).This model underlies the fractal derivative model of Reynold turbulence equation relative to the corresponding fractional derivative model.