We study the effect of node mobility on the throughput scaling of the covert communication over a wireless adhoc network. It is assumed that n mobile nodes want to communicate each other in a unit disk while keeping the presence of the communication secret from each of Theta(ns) non-colluding wardens (s > 0). The wardens can be mobile or fixed. Our results show that the node mobility greatly improves the throughput scaling, compared to the case of fixed node location. In particular, for s <= 1, the aggregate throughput scaling, i.e., the maximally achievable throughput scaling of the total network when each source-destination pair communicates with the same rate, is shown to be arbitrarily close to linear in n when the number of channel uses l that each warden uses to judge the presence of communication is not too large compared to n. More specifically, the aggregate throughput scaling is arbitrarily close to linear when s <= 1 and l = O(n((alpha-2)(1-s))), where alpha >= 2 denotes the path loss exponent. For the achievability, we modify the two-hop based scheme by Grossglauser and Tse (2002), which was proposed for a wireless ad hoc network without a covertness constraint, by introducing a preservation region around each warden in which the senders are not allowed to transmit and by carefully analyzing the effect of covertness constraint on the transmit power and the resultant transmission rates. This scheme is shown to be optimal for 0 < s <= 1 under an assumption that each node outside preservation regions around wardens uses the same transmit power.