Abstract: The spacecraft reachable domain (RD) is an effective method to present the possible position boundary of a spacecraft in a future time, which is of great significance for maintaining the safety of spacecraft and improving the ability of space situational awareness. However, previous research efforts on solving RD still have some disadvantages, e.g. some RD models are relatively complicated, and some other solving methods are highly sensitive to the initial values thus result in poor computational accuracy. Therefore, it is necessary to develop a more concise and efficient RD solving algorithm. This paper develops an innovative model to solve the RD based on the extremum condition of the predicted position vector, in the pericenter coordinate frame. First, a vector description method is defined to express the spatial orientation and the criterion of accessibility for an arbitrarily given position vector. Second, the maneuvering azimuth angle in the transfer-orbit plane is used to transform the reachable domain problem to the univariate extreme value problem, at the current accessible position vector. The value of the maneuvering azimuth is determined by considering that the gradient of the describing function at the surface of RD envelope is zero, following this, the maneuvering reachable domain of the spacecraft with a single impulse can be obtained. In addition, the symmetry of the RD envelope under two-body dynamical assumption is used to reduce the computational complexity. Finally, the RD solving algorithm proposed in this paper is verified by Monte Carlo simulation. The numerical results show that the new RD algorithm proposed in this paper provides good agreement with the Monte Carlo simulation on computational accuracy. Moreover, the new RD algorithm is more concise and more accurate than the existing RD solving methods.