Conventional and license-free radio-controlled drone activities are limited to a line-of-sight (LoS) operational range. One of the alternatives to operate the drones beyond the visual line-of-sight (BVLoS) range is replacing the drone wireless communications system from the conventional industrial, scientific, and medical (ISM) radio band to a licensed cellular-connected system. The Long Term Evolution (LTE) technology that has been established for the terrestrial area allows command-and-control and payload communications between drone and ground station in real-time. However, with increasing height above the ground, the radio environment changes, and utilizing terrestrial cellular networks for drone communications may face new challenges. In this regard, this paper aims to develop an LTE-based control system prototype for low altitude small drones and investigate the feasibility and performance of drone cellular connectivity at different altitudes with measuring parameters such as latency, handover, and signal strength. The measurement results have shown that by increasing flight height from ground to 170 m the received signal power and the signal quality levels were reduced by 20 dBm and 10 dB respectively, the downlink data rate decreased to 70%, and latency increased up to 94 ms. It is concluded that although the existing LTE network can provide a minimum requirement for drone cellular connectivity, further improvements are still needed to enhance aerial coverage, eliminate interference, and reduce network latency.