Two components of jets associated with the afterglow of the gamma-ray burst GRB 160623A were observed with multi-frequency observations including long-term monitoring in a sub-millimetre range (230 GHz) using the SMA. The observed light curves with temporal breaks suggests on the basis of the standard forward-shock synchrotron radiation model that the X-ray radiation is narrowly collimated with an opening angle $theta_{n,j}<sim6^{circ}$ whereas the radio radiation originated from wider jets ($sim27^{circ}$). The temporal and spectral evolutions of the radio afterglow agree with those expected from a synchrotron radiation modelling with typical physical parameters except for the fact that the observed wide jet opening angle for the radio emission is significantly larger than the theoretical maximum opening angle. By contrast, the opening angle of the X-ray afterglow is consistent with the typical value of GRB jets. Since the theory of the relativistic cocoon afterglow emission is similar to that of a regular afterglow with an opening angle of $sim30^{circ}$, the observed radio emission can be interpreted as the shocked jet cocoon emission. This result therefore indicates that the two components of the jets observed in the GRB 160623A afterglow is caused by the jet and the shocked jet cocoon afterglows.
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