Vehicular Cloud Computing (VCC) is a new technological shift which exploits the computation and storage resources on vehicles for computational service provisioning. Spare onboard resources are pooled by a VCC operator, e.g. a roadside unit, to serve computational tasks using the vehicle-as-a-resource framework. This paper investigates timely service provisioning for deadline-constrained tasks in VCC systems by leveraging the task replication technique (i.e., allowing one task to be executed by vehicles). A learning-based algorithm, called DATEV (Deadline-Aware Task rEplication for Vehicular Cloud), is proposed to address the special issues in VCC systems including uncertainty of vehicle movements, volatile vehicle members, and large vehicle population. The proposed algorithm is developed based on a novel contextual-combinatorial multi-armed bandit learning framework. DATE-V is ' contextual ' because it utilizes side information (context) of vehicles and tasks to infer the completion probability of a task replication under random vehicle movements. DATE-V is 'combinatorial' because it replicates the received task and sends task replications to multiple vehicles to guarantee the service timeliness. When learning with multi-armed bandit, DATE-V also addresses the practical concern of delayed feedbacks caused by the task transmission/computational delay in using VCC. We rigorously prove that our learning algorithm achieves a sublinear regret bound compared to an oracle algorithm that knows the exact completion probability of any task replications. Simulations are carried out based on real-world vehicle movement traces and the results show that DATE-V significantly outperforms benchmark solutions.