In the paper, we introduce a new concept of poly-Bernoulli numbers and polynomials of the second kind which is called Hermite poly-Bernoulli numbers and polynomials of the second kind. We also investigate and analyse its applications in number theory, combinatorics and other fields of mathematics. The results derived here are a generalization of some known summation formulae earlier studied by Jolany et al. [17,18], Dattoli et al [14] and Pathan et al [29,30]. Keywords:Hermite polynomials, poly-Bernoulli polynomials of the second kind, Hermite poly-Bernoulli polynomials of the second kind, summation formulae, symmetric identities Cite This Article: