In this paper, we propose a multilayered Long Short-Term Memory (LSTM) architecture with parameter transfer for a traffic speed data imputation in the vehicle to infrastructure (V2I) networks. We consider a scenario in V2I networks where a Road Side Unit (RSU) on the road cannot temporarily collect the traffic speed data because of its malfunction, which causes services that use the traffic speed data at the RSU to be unavailable. Therefore, it is imperative to develop an efficient and low complexity data imputation algorithm for uninterrupted and seamless V2I services. We propose an architecture that uses a multilayered LSTM (M-LSTM) network with parameter transfers, which can explicitly consider the characteristics of temporal dependency in the traffic speed data. The temporal dependency of the traffic speed data enables the parameters trained from each LSTM layer to be transferred to its adjacent LSTM layer and used for its parameter training, thereby significantly reducing the overall training and imputing complexity. Our simulation and experiment results confirm that the time for training and data imputation can be significantly reduced while maintaining imputation accuracy.