The experimental demonstration of the formation of a strong electrostatic (ES) collisionless shock has been carried out with high-speed counterstreaming plasmas, produced by a high-power laser irradiation, without external magnetic field. The nearly four times density jump observed in the experiment shows a high Mach-number shock. This large density jump is attributed to the compression of the downstream plasma by momentum transfer by ion reflection of the upstream plasma. Particle-in-cell (PIC) simulation shows the production of a collisionless high Mach-number ES shock with counterstreaming interaction of two plasma slabs with different temperatures and densities, as pointed out by Sorasio et al. [Phys. Rev. Lett. 96, 045005 (2006)]. It is speculated that the shock discontinuity is balanced with the momentum of incoming and reflected ions and the predominant pressure of the electrons in the downstream with PIC simulation.