Multifunctional radar is a trend in the future. Employing radar system for high data rate, long range, anti-intercepted communication by making use of its wide bandwidth, high power and directing property has been a research hotspot nowadays. Hereinto, radar-communication compatible waveforms design is a key technique. This paper proposes a novel compatible waveform produced by modulating LFM signal by MSK and mainly explores its ambiguity function (AF) and impacts of the AF by parameters of the waveform. Keeping the total pulse width and LFM coefficient constant, theory analysis and simulations show properties as follows: 1. AF of modulating LFM is closer to thumbtack shape than that of non-modulating LFM. 2. The larger the bit number, the closer to the thumbtack shape the AF is. 3. Whether modulating or not, resolutions of Doppler and delay are the same. 4. For zero Doppler slice, the larger bit number results in the more suppression of the side lobes near to the main lobe. From these properties, it can obtain a good radar waveform of which AF is closer to thumbtack shape by increasing bit number.