To decrease the uncertainty of localization and mapping of UAV at the same time, and to increase the speed of searching the unknown environment at which UAV locates, an active SLAM trajectory programming algorithm is proposed based on optimal control. With all the factors considered, UAV SLAM is taken as a combined optimization problem to achieve the global optimization by designing a new objective function, by use of the representations of average information gain and new search landmark environment. This algorithm is validated based on the simplified UAV plan