Point cloud filtering is a preliminary and essential step in various applications of airborne LiDAR (light detection and ranging) data, with progressive triangulated irregular network (TIN) densification (PTD) being one of the classic methods for filtering LiDAR point clouds. The PTD algorithm densifies ground points through iteration operation based on initial ground seed points. However, the poor performance in steeply sloped areas and time-consuming processing are serious drawbacks for PTD algorithms. In this paper, we propose a fast progressive TIN densification (FPTD) filtering algorithm for airborne LiDAR data using adjacent surface information. After carefully establishing parameters and removing outliers, our improved FPTD uses a sliding window to obtain significantly more initial ground seed points. And we modified some iterative determination criterion , including the definition of maximum relative elevation threshold and the introduction of signed computation, to eliminate avoidable non-ground points. Then adjacent surface information was utilized to iterate each point cloud block, which is the smallest unit that point cloud can be segmented. Additionally, the algorithm is easily run in a multi-threaded environment, further accelerating the filtering process to some extent. Experiments show that our proposed FPTD filtering algorithm is fast and robust. Compared to the PTD, the FPTD algorithm yields better error rates and kappa coefficients in 1/12 of the time required by the PTD.