Quadcopters are four propellers unmanned aerial vehicles (UAVs) which have various applications such as rescue, remote sensing, and surveying. Providing stability and reliable tracking performance are among important criteria in the controller designs for these systems. Proportional integral derivative (PID) controller is one of the commonly used schemes to create a stable movement for UAVs. Utilizing this controller requires a precise tuning and initialization of its parameters. An optimized tuning of PID controller coefficients leads to an appropriate performance trajectory for quadcopter. In this paper, optimal tuning of quadcopter’s PID controller gains is investigated, which is previously performed by classic methods such as Ziegler-Nichols (ZN) and primary metaheuristic algorithms like Genetic Algorithm (GA), the Crow Search Algorithm (CSA), and Particle swarm Optimization (PSO). An improved Biogeography-Based Optimization (BBO) algorithm is proposed to design a PID controller and stabilize the movements of quadcopters. Numerical results indicate that the controller is stable and effective.