According to the airspace classification by the Federal Aviation Agency, Class G airspace is the airspace at 1,200 feet or less to the ground, which is beneath class E airspace and between classes B-D cylinders around towered airstrips. However, the lack of flight supervision mechanism in this airspace, unmanned aerial system (UAS) missions pose many safety issues. Collision avoidance and route planning for UASs in class G airspace is critical for broad deployment of UASs in commercial and security applications. Yet, unlike road network, there is no stationary marker in airspace to identify corridors that are available and safe for UASs to navigate. In this paper, we present an automatic LiDAR-based airspace corridor construction method for navigation in class G airspace and a method for route planning to minimize collision and intrusion. Our idea is to combine LiDAR to automatically identify ground objects that pose navigation restrictions such as airports and high-rises. Digital terrain model (DTM) is derived from LiDAR point cloud to provide an altitude-based class G airspace description. Following the FAA Aeronautical Information Manual, the ground objects that define the restricted airspaces are used together with digital surface model derived from LiDAR data to construct the aerial corridor for navigation of UASs. Preliminary results demonstrate competitive performance and the construction of aerial corridor can be automated with much great efficiency.