In order to further enhance the detection performance of radar for moving targets on the ground and to achieve spectral coexistence between radar and communication systems, the waveform design is studied for spectral coexistence of airborne Multiple-Input Multiple-Output (MIMO) radar under condition of the environment of ground clutter. Firstly, the peak-to-average-power ratio (PAR) constraint is exerted on the waveform,and then both the global spectrum design and the local spectrum design are considered. Finally, a novel cyclic iterative algorithm is proposed. In process of each iteration, the original nonconvex optimization problem is transformed into a solvable convex optimization problem through the convex approximation, and then the optimal solution of the waveform is obtained directly by using the Feasible Point Pursuit Successive Convex Approximation（FPP-SCA）algorithm. The simulation results show that compared with the existing algorithm, the algorithm not only has still faster operation speed, but also can play a role of PAR constraint in waveform.