Given a simple connected graph G with n vertices, the spanning tree problem involves finding a tree that connects all the vertices of G. Solutions to this problem have applications in electrical power provision, computer network design, circuit analysis, among others. It is known that highly efficient sequential or parallel algorithms can be developed by restricting classes of graphs. Circular trapezoid graphs are proper superclasses of trapezoid graphs. In this paper, we propose an O(n) time algorithm for the spanning tree problem on a circular trapezoid graph. Moreover, this algorithm can be implemented in O(log n) time with O(n/ log n) processors on EREW PRAM computation model.