Abstract: A new projection algorithm is proposed to solve the nonmonotone equilibrium problem in the real Hilbert space. The global weak convergence of the sequences generated by the algorithm does not require the bifunction to satisfy any monotonicity condition, but only requires the solution set of the associated Minty equilibrium problem is nonempty. The new algorithm saves the computational cost of calculating the next iteration point of the known algorithm (DHF for short) algorithms. Under the same assumptions with DHF, the weakly global convergence of the sequence generated by this new algorithm is established. Numerical experiments show that the new algorithm is more efficient than DHF from CPU time point of view.