We propose edge expansion parallel cascade selection molecular dynamics (eePaCS-MD) as an efficient adaptive conformational sampling method to investigate the large-amplitude motions of proteins without prior knowledge of the conformational transitions. In this method, multiple independent MD simulations are iteratively conducted from initial structures randomly selected from the vertices of a multi-dimensional principal component subspace. This subspace is defined by an ensemble of protein conformations sampled during previous cycles of eePaCS-MD. The edges and vertices of the conformational subspace are determined by solving the "convex hull problem." The sampling efficiency of eePaCS-MD is achieved by intensively repeating MD simulations from the vertex structures, which increases the probability of rare event occurrence to explore new large-amplitude collective motions. The conformational sampling efficiency of eePaCS-MD was assessed by investigating the open-close transitions of glutamine binding protein, maltose/maltodextrin binding protein, and adenylate kinase and comparing the results to those obtained using related methods. In all cases, the open-close transitions were simulated in ∼10 ns of simulation time or less, offering 1-3 orders of magnitude shorter simulation time compared to conventional MD. Furthermore, we show that the combination of eePaCS-MD and accelerated MD can further enhance conformational sampling efficiency, which reduced the total computational cost of observing the open-close transitions by at most 36%.