For the issue that the distance-based approaches of connectivity preservation are too conservative a leader-follower formation control approach is proposed for second-order multi-agent systems with improved connectivity preservation.Firstlyconsidering that not all followers can receive information from the leadera desired offset position based distributed formation control protocol is designed.Nextby utilizing the position and velocity of the agents simultaneouslya judgment method of connectivity trend is proposed.Furthermorean adaptive action function based on relative velocity and distance is designed.Compared with traditional connectivity preservation methods based on artificial potential fieldthe proposed method can accurately determine the trend of connectivity between the agentsand reduce the adverse effects on the formation.Finallythe sufficient conditions for the stability of the system are given by using graph theoryand the superiority of the proposed method is verified through numerical simulation and comparative experiment.