The observations of jet breaks in the afterglows of short gamma-ray bursts ( SGRBs ) indicate that the jet has a small opening angle of \lesssim 10 ^ { \circ } . The collimation mechanism of the jet is a longstanding theoretical problem . We numerically analyze the jet propagation in the material ejected by double neutron star merger , and demonstrate that if the ejecta mass is \gtrsim 10 ^ { -2 } M _ { \odot } , 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 low-luminous new types of event . By constructing a model for SGRB 130603B , which is associated with the first kilonova/macronova candidate , we infer that the equation-of-state of neutron stars would be soft enough to provide sufficient ejecta to collimate the jet , if this event was associated with a double neutron star merger .