We have derived a new equation of state (EOS) based on the Eulerian finite scheme utilizing the 3/2th power of edge length by pressure. By truncating the order of finite strains in the expression of the Helmholtz free energy, we have derived new expressions for second- and third-order EOSs, as well as expressions for bulk modulus and its first pressure derivative. We have considered four materials, viz. CaO, Bi, NaCl and Fe$_2$SiO$_4$ to test the applicability and validity of the derived EOS. The feature of this EOS shows more validity than other prominent EOSs and corresponds well with the available experimental results.