The channel estimation in the IEEE 802.11p vehicle-to-everything (V2X) communication systems is generally a challenging task due to high mobility and insufficient number of pilots. Conventional data pilot-aided channel estimation schemes are difficult to apply in practice due to high complexity and the error propagation problem. In this correspondence paper, we propose a new data pilot-aided channel estimation scheme to overcome both issues. To this end, we develop a state feedback decision algorithm that enables us to extract reliable data pilots within a few received symbols. As a result, we can minimize both the error propagation effect and the computational complexity. We verify the complexity gain of the proposed scheme through the complexity analysis. Finally, we demonstrate the accuracy of the proposed channel estimation scheme in terms of the packet error rate performance.