Silicene, a buckled two-dimensional honeycomb structure of silicon, has been experimentally synthesized on very few substrates. Furthermore, synthesizing silicene with a Dirac point is another hot research area. However, only silicene grown on Ag(111) has been reported to have a Dirac point, which has lowered the expectations of researchers. Here, three Si monolayer structures, a Si chain-type structure, a two-dimensional hexagonal close packed compound structure, and a two-dimensional hexagonal close packed structure, are generated on a c-BN(111) substrate using a particle-swarm optimization algorithm implemented in CALYPSO code. Band structure calculations show that all three structures exhibit a metallic nature. In particular, due to the absolutely flat conformation of the latter two structures, a linear dispersion exists near the Fermi energy level, indicating that charge carriers can transport like massless Dirac fermions. Our results open an alternative way of searching for other two-dimensional silicon monolayers with Dirac points.