One of the important use-cases of 5G network is the vehicle to infrastructure (V2I) communication which requires accurate understanding about its dynamic propagation environment. As 5G base stations (BSs) tend to have multiple antennas, they will likely employ beamforming to steer their radiation pattern to the desired vehicle equipment (VE). Furthermore, since most wireless standards employ an OFDM system, each VE may use one or more sub-carriers. To this end, this paper proposes a joint design of adaptive channel prediction, beamforming and scheduling for 5G V2I communications. The channel prediction algorithm is designed without the training signal and channel impulse response (CIR) model. In this regard, first we utilize the well known adaptive recursive least squares (RLS) technique for predicting the next block CIR from the past and current block received signals (a block may have one or more OFDM symbols). Then, we jointly design the beamforming and VE scheduling for each sub-carrier to maximize the uplink channel average sum rate by utilizing the predicted CIR. The beamforming problem is formulated as a Rayleigh quotient optimization where its global optimal solution is guaranteed. And, the VE scheduling design is formulated as an integer programming problem which is solved by employing a greedy search. The superiority of the proposed channel prediction and scheduling algorithms over those of the existing ones is demonstrated via numerical simulations.