In this manuscript, the conventional combined heat and power economic dispatch (CHPED) problem is reconsidered under fuel constraint with take-or-pay contract. The aim of the problem is to find the optimal active power generations and heat productions which provides the minimum fuel cost while satisfying all operational constraints. A recently presented metaheuristic approach, Marine Predators Algorithm (MPA), is chosen for solving the problem addressed. Unlike the previous studies dealing with the CHPED problem, ramp rate, valve-points effect, prohibited operation zones for power-only units, feasible region constraints of combined heat and power units, take-or-pay constraint for limited fuel supply units are included all at once. Furthermore, power transmission losses are calculated using B-matrix loss formula. Case studies are conducted on a 24-unit test system with a 24-h operation period. The results obtained for the cases with and without the take-or-pay constraint are compared. When the take-or-pay constraint is taken into account, a 3.5% saving is achieved in the total cost.