<p>The quark gluon plasma as a unique state of matter is investigated in the extended quasiparticle model by the momentum-dependent interaction. The self-consistent thermodynamics is realised through an effective bag constant. The equation of state and the speed of sound are calculated for different sets of quark mass scales and coupling constants. It is found that the equation of state becomes hard and close to the Stefan–Boltzmann (SB) limit with the combination effect of the momentum-dependent factor and the running coupling interactions. Moreover, the corresponding sound velocity is more close to the lattice simulation result. It is concluded that the momentum-dependent scale and the running coupling interaction are necessary for the quasiparticle model to be consistent with the lattice result.</p>