Nowadays unmanned aerial vehicles (UAV's) are increasingly considered in several engineering and safety applications to explore unknown environments. Forest environments are among these environments of interest where autonomous exploration and navigation is desirable with the caveat that GPS may not be accessible for localization of the drone. Motivated by the latter, in this paper we present a methodology for autonomous navigation of UAV in forest environments, paying particular attention to competences desired in autonomous navigation, namely detection and evasion of trees. Obstacle detection is performed using a deep neural network approach trained with a limited database but that exploits transferred learning from a well-known network architecture called Alexnet. In addition to the detection of a tree, a direction of avoidance is also recognized, this is, evasion to the left or to the right is obtained with the same learning scheme. Our approached was assessed in simulation by using the simulator Gazebo and also in a real outdoors scenario populated with trees.