This paper develops a framework for vessel surveillance video uploading via maritime wideband communication networks. A broadband wireless network utilizing a time-division-multiple-access (TDMA)-based media access control protocol is employed to establish a shore-side network infrastructure, and a packet store-carry-forward routing mechanism is adopted to achieve intermittent network connectivity in maritime communications. To provide high-quality videos to the administrative authority, a resource allocation problem is formulated to maximize the throughput priority-based video transmission problem, subject to the intermittent network connections and the time indexes such as the release time and deadline of each video packet. To reduce computational complexity, time-capacity mapping is applied to transform the original resource allocation problem into a two-machine nonpreemptive scheduling problem. Three offline scheduling algorithms are proposed, namely, a time-capacity-mapping-based two-phase (TMTP) algorithm for a single machine, a TMTP algorithm for two machines, and an interval graph-theory-based job relay selection (IGTJRS) algorithm. It is mathematically proved that the IGTJRS algorithm has an approximation ratio (i.e., the ratio of the throughput of an optimal schedule to that of the IGTJRS algorithm) of 2 and time complexity of O(n²). Simulations results validate the performance of the proposed algorithms, based on real ship route traces obtained from navigation software BLM-Shipping.