Aeronautical short message (ASM), as a critical service for the future 4 dimensional trajectory data link (4DTRAD), will meet a great challenge of transmission efficiency. In order to achieve an efficient usage of wireless resources, in this paper a preempting transmission strategy based on the distributed mapping algorithm (PT-DMA) is proposed for the L-band digital aeronautical communication system type-1 (LDACS1). By using the proposed PT-DMA, allocated continuous time slots could be re-mapped discretely within a multiframe. Then, a preempting strategy is further studied based on distributed time slots, with which the real time performance and capacity improvement of ASM on LDACS1 could be expected. Note that the discrete mapping will not change the fundamental framework of LDACS1 request-allocation mechanism. Numerical results confirm that the PT-DMA will meet less time delay and obvious capacity improvement in ASM transmission.