In this paper, we present a tomographic reconstruction method to reduce a tomographic error, multi time-stepreconstruction, for a wide-eld adaptive optics (WFAO). Based on the frozen ow assumption, we can computethe time evolution of measurements from wave-front sensors (WFS) at previous time-steps with using windinformation. Our idea is to reduce the tomographic error by using the measurements at both the current andprevious time-steps simultaneously. We also develop a method to estimate wind speed and direction at eachaltitude from temporal correlations of phase distortion pattern reconstructed by a classical tomography. Weevaluate the performance of the method by a laboratory experiment with the RAVEN, a multi-object adaptiveoptics (MOAO) technical and science demonstrator. In the laboratory experiment, our wind estimation methodcan estimate wind speeds and directions of multiple layers. By the multi time-step reconstruction method, theensquared energy in a 140 mas box increases about 3{5% compared with a classical tomographic reconstruction.