Seismic reservoir characterization has been extensively employed during the last decades. Beside the deterministic seismic inversion, and to quantify the uncertainty, the multi-realization inversions have been recently taken into account. 3D Geostatistical modeling of Acoustic Impedance (AI) based on only well data might introduce significant uncertainties. To overcome at this issue, seismic attributes might be useful, since it is the direct measurement of subsurface. To involve the seismic data in this procedure, the co-estimation approaches such as co-kriging, or the co-simulation algorithms are typically employed. In this paper, Turning Bands Co-Simulation (TBCo-Sim) is used that can perform co-simulation of multi-variable data. TBCo-Sim is fast and reproduces the geostatistical parameters (e.g. variograms and histogram) more accurately compared with similar conventional algorithms. In order to use the most related seismic attributes, stepwise linear multi-attribute transform is carried out to construct a new meta-attribute. Subsequently, 3D AI modelling is performed, and hence, different realizations of AI are generated. The correlation coefficient of mean of realizations with AI at the test wells are above 93%. Therefore, we would recommend TBCo-Sim and stepwise multi-attribute transform as a novel and powerful algorithm for AI modelling during multi-realization seismic inversion.