A short packet transmission is one of the major operational modes for mission-critical data in ultra reliable and low latency communications (URLLCs) and control-type data in massive machine-type communications (mMTCs). The central challenge in the short packet transmission is the excessive amount of overhead caused by the pilot signaling. In this letter, we propose a novel transmission scheme that does not require the pilot signaling, called pilot-less sparse vector coding (PL-SVC). Key feature of PL-SVC is to map the input as a composite of the sparse vector and the fading channel and to perform decoding by finding out the nonzero positions of a sparse vector. In this setting, the system matrix becomes a pseudo-random spreading matrix and the input vector becomes a channel-scaled sparse vector so that the PL-SVC decoding problem can be cast into the support detection problem in the compressed sensing. We show from numerical experiments in the 5G uplink scenario that PL-SVC is very effective in the short packet transmission and outperforms conventional schemes.