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In this paper, we compute the constrained QCD effective potential up totwo-loop order with finite quark mass and chemical potential. We present theexplicit calculations by using the double line notation and analyticalexpressions for massless quarks are obtained in terms of the Bernoullipolynomials or Polyakov loops. Our results explicitly show that the constrainedQCD effective potential is independent on the gauge fixing parameter. Inaddition, as compared to the massless case, the constrained QCD effectivepotential with massive quarks develops a completely new term which is onlyabsent when the background field vanishes. Furthermore, we discuss the relationbetween the one- and two-loop constrained effective potential. The surprisinglysimple proportionality that exists in the pure gauge theories, however, is ingeneral no longer true when fermions are taken into account. On the other hand,for high baryon density $\mu_B$ and low temperature $T$, in the massless limit,we do also find a similar proportionality between the one- and two-loopfermionic contributions in the constrained effective potential up to ${\calO}(T/\mu_B)$.

Two-loop perturbative corrections to the constrained effective potential in thermal QCD