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The observations of jet breaks in the afterglows of short gamma-ray bursts (SGRBs) indicate that the jet has a small opening angle of [<, ~]10[degrees]. The collimation mechanism of the jet is a longstanding theoretical problem. We numerically analyze the jet propagation in the material ejected by a double neutron star (NS) merger, and demonstrate that if the ejecta mass is [> ~]10 super(-2) M sub([middot in circle]), the jet is well confined by the cocoon and emerges from the ejecta with the required collimation angle. Our results also suggest that there are some populations of choked (failed) SGRBs or new types of events with low luminosity. By constructing a model for SGRB 130603B, which is associated with the first kilonova/macronova candidate, we infer that the equation of state of NSs would be soft enough to provide sufficient ejecta to collimate the jet, if this event is associated with a double NS merger.