To solve the complex problem of multi-projectile-multi-phase cooperative trajectory programming, an augmented centralized collaborative trajectory programming method (AC-CTPM) is proposed. Firstly, a five-phase trajectory programming model is established based on the characteristics of each phase in the flight process of guided projectiles. Then, the five-phase trajectory programming problems of n_p guided projectiles are combined and extended to a more complex 5np phases optimal control problem (OCP). The multi-phase Radau pseudo-spectral method is used to discretize the infinite-dimensional OCP into a finite-dimensional nonlinear programming problem (NLP), which is finally solved using the mature NLP solver SNOPT. To improve the efficiency of solving the complex 5n_p phases OCP, in AC-CTPM, we propose an initial guess value acquisition method (IGVAM) for converting 2D scheme trajectories into 3D predicted trajectories in cooperative trajectory programming problem. Each guided projectile establishes a new ground coordinate system with its own launch point as the origin. Within this new coordinate system, 2D scheme trajectories of the projectile are rapidly programmed. Subsequently, by expanding and transforming the coordinates, the programmed 2D trajectories in the new coordinate system are transformed into the 3D scheme trajectory. The 3D scheme trajectories of each projectile are combined to form the initial prediction of the cooperative trajectory programming problem. By applying the AC-CTPM algorithm, we conducted simulation-based solving for the scenario of simultaneous impact tasks with single-gun multiple-firing and multiple-gun salvo. We obtained cooperative trajectory solutions that satisfy the projectile self-constraints and cooperative constraints, which verifies the effectiveness of AC-CTPM algorithm. Simulation comparisons with distributed collaborative trajectory programming algorithm (D-CTPM) and traditional centralized collaborative trajectory programming algorithm (TC-CTPM) shows that the objective function of the cooperative scheme trajectory programmed by AC-CTPM algorithm is on average 5.07% better than that of TC-CTPM algorithm and 32.98% better than that of D-CTPM algorithm on average, while the solution time of the AC-CTPM algorithm is reduced by 86.48% compared with TC-CTPM algorithm and by 82.36% compared with D-CTPM algorithm, which verifies the superiority of the AC-CTPM algorithm.