Massive machine type communications (mMTC) is a service category in 5G to support Internet of Things (IoT). Typically, mMTC-based services require small volume of information. Since the current data transmission principle requires long codeblock to maximize the coding gain and hence is not adequate for short packet transmission, multiplexing mechanism to support short packet transmission in mMTC is required. In this paper, we propose a new type of uplink data transmission scheme suitable for the mMTC, called sparse vector coding (SVC). Key idea behind the proposed technique is to transmit the information after the sparse transformation. By mapping the information into the sparse vector and then transmitting it after the random non-orthogonal spreading, we cast the symbol detection problem into the sparse signal recovery problem in compressed sensing. We show from the simulations in the LTE uplink scenario and massive access scenario in 5G that the proposed SVC scheme outperforms conventional approaches and is very effective in short packet transmissions.