In this paper, we introduce a new class of generalized Hermite-Euler and Hermite-Genocchi polynomials and derive some symmetric identities by applying the generating functions. Also, we obtain some potentially useful relations for the Bernoulli polynomials, Euler polynomials, power sum, alternating sum and Genocchi numbers. These results extend some known summations and identities of generalized Hermite-Euler and Hermite-Genocchi polynomials studied by Dattoli et al. [3], Pathan and Khan [9] and Khan [5].