We study the charmonium dissociation in the hot medium with finite baryon chemical potential µB. Charmonium bound states are dissociated in the medium by the color screening effect and parton random scatterings. When the medium quark chemical potential µq = µB/3 is large compared with the temperature, the real part of heavy quark potential is reduced, which acts as the role of a stronger color screening. Charmonium wave package expands outside due to the weak attractive potential at finite µq and T . J/ψ fractions defined as the quantum overlap between the wave package and the wave function of J/ψ eigenstate decreases with time due to the reduced real part of the potential and the imaginary potential. We include the above hot medium effects to calculate the J/ψ survival probability in the static medium and the Bjorken medium with fixed values of µq. J/ψ survival probability is reduced by the µq-term at low temperatures and large µB, while this effect becomes not apparent at high temperatures.