  We derive an exact black hole solution for the Einstein-Gauss-Bonnet gravity
with Yang-Mills field in $4D$ AdS spacetime and investigate its thermodynamic
properties to calculate exact expressions for the black hole mass, temperature,
entropy and heat capacity. The thermodynamic quantities get modification in the
presence of Yang-Mills field, however, entropy remains unaffected by the
Yang-Mills charge. The solution exhibits $P-v$ criticality and belongs to the
universality class of Van der Waals fluid. We study the effect of Gauss-Bonnet
coupling and Yang-Mills charge on the critical behaviour and black hole phase
transition. We observe that the values of critical exponents increase with the
Yang-Mills charge and decrease with the Gauss-Bonnet coupling constant.
