Lambert’s problem is one of the classical methods for solving the multiple revolution problem in orbit determination. With the increasing interest in space exploration programs and using satellite networks, it is important to provide an accurate and rapid method that will provide the network control center with information regarding the orbit of each satellite in the network and help the satellites improve routing decisions in onboard processing satellites. Lambert’s problem is one of the methods that solve the problem iteratively and this iteration was originally done using Newton’s iteration method. In recent studies, it is recommended to use the Chebyshev-Picard iteration method to solve this problem. Since the aim here is to provide a method that solves the problem rapidly, the Chebyshev-Picard iteration method serves our objective since it is highly parallelizable. In this work, we have developed a parallel algorithm that solves Lambert’s problem in a parallel environment. We have conducted experiments to demonstrate the parallel scalability of the algorithm on both shared and distributed memory architectures. The experimental results show that the parallel algorithm achieves 8.26- and 3.94-times faster execution time on distributed memory and shared memory architectures, respectively.