In this work, we consider the problem of finding a meta-learning online control algorithm that can learn across the tasks when faced with a sequence of N (similar) control tasks. Each task involves controlling a linear dynamical system for T time steps. The cost function and system noise at each time step are adversarial and unknown to the algorithm before taking the control action. The goal of a meta-learning algorithm is to sequentially prescribe the individual online control policies for each new task by exploiting the information from previous tasks and the property of task similarity. We propose a meta-learning online control algorithm for this setting and characterize its performance using the metric of meta-regret, which is the average cumulative regret of the tasks. We show that, when the number of tasks are sufficiently large, the meta-regret of our proposed approach is smaller by a factor D/D* compared to an independent-learning online control algorithm which does not perform learning across the task, where D is a problem constant and D* is a scalar that decreases with increase in task similarity. Thus, when the sequence of tasks are similar, the regret of the proposed meta-learning online control is significantly lower than that of the naive approaches without meta-learning. We also present numerical results to demonstrate the superior performance achieved by our meta-learning algorithm.