We have simulated the random walk in one dimensional and three dimensional lattices by applying suitable external biases. A suitable analytical formula for integrating bias with random walk is formulated. Different regime of transport called diffusion and drift regime are identified. By analyzing the mean square difference with time we have identified a time called transition time, where the nature of motion changes from diffusion like to drift like. The biases are scanned in the sale of 0 to 1 and analyzed the variation of transition time with magnitude of bias. It is shown that the effect of bias is more prominent in case of one dimension. This is explained with the help of dependent of random walk properties on the angle between external bias and direction of random walk. This type of study is helpful for the analysis of various systems like semiconductors, plasma, random laser etc.