This study describes a generation of globally time optimal trajectories for a mobile robot in predefined environment. The primary task in the study is to apply Differential Evolution (DE) method for definition of globally time-optimal trajectories under environmental and dynamical constraints. The planned trajectories are composed of line segments and curve segments. The structures of the curve segments are determined by using only two parameters such as a turn angle theta and a translation velocity on the curve v(t)_(start) All possible curve segments in parameters range theta is an element of (0, pi)degrees, v(t)_(start) [0,40] inch and a(t)_(turn) is an element of[-a(t)_(max),a(t)_(max)] inch/sec(2) form a curve segments set. Then DE, is used to find time optimal trajectory from this set. Experimental results are given and the results are shown successfully.