Dielectric elastomeric actuators (DEAs) have been intensely studied in the recent decades. Their attractive features include large deformation(380%), large energy density(3.4 J/g), light weight, fast response( 1 ms), and high efficiency (80%-90%). They can be used in medical devices, space robotices and energy harvesters. The core part of DEAs is a dielectric elastomeric film with two electordes. When pre-stretched forces are exerted on the film in plane direction and voltage is applied across its thickness, the film achieves a large deformation. Usually the effect of electric field is described by Maxwell stress E2, and the effect of mechanical field is described by free energy function models (such as Neo-Hookean model, Arruda-Boyce model and Gent model). There are deviations in varying degree between every models and tests of dielectric elastomer. No model works perfectly. In the present paper, a new free energy function model is given to reduce the deviation. According to the main models above, an undetermined parameter C(1, 2) is introduced. and i (W/i)= C( 1, 2)(i2- 1-2 2-2), pi = C( 1, 2)( pi2- p1-2p2-2)(i/ pi), i = 1, 2, are assumed. The new i ( W/i) and pi are substituted into the equation of equilibrium of dielectric elastomer film pi + E2 = i ( W/i), i = 1, 2. Under equal-biaxial pre-stretched condition, P1 = P2 = P, p1 = p2 = p, C(1, 2) = C(). The parameter C()= (V2/t0)2/( 2- -4-( p- p-4)(/ p)) is obtained. Through analysing the test results of VHB4905 which contains a series of equal-biaxial pre-stretched tests, the data (, C()) are obtained from the test data (, V). C() =a + beI1-3, (I1 = 12 + 22 + 32) can be determined by data points (, C()). By computing the integral of i ( W/i)= a + beI1-3)(i2- 1-2 2-2), i = 1, 2, a new free energy function W = (a/2)(I1-3) + b[eI1-3(I1-3-1) + 1] (the new model) is achieved. The test results of VHB4905 are fitted by Neo-Hookean, Gent model and the new model. Neo-Hookean model fits well only in small deformation. Gent model fits well only in small-middle deformation, and does not work well when stretch 3.5. The new model fits well in small, middle and large deformation. It is better than Neo-Hookean and Gent model. The new model can give big support in the study of dielectric elastomer materials and structure property, and can be used in engineering practice effectively.