In this paper, we study Hermitian linear complementary dual (abbreviated Hermitian LCD) rank metric codes. A class of Hermitian LCD generalized Gabidulin codes are constructed by qm-self-dual bases of Fq2m over Fq2. Moreover, the exact number of qm-self-dual bases of Fq2m over Fq2 is derived. As a consequence, an upper bound and a lower bound of the number of the constructed Hermitian LCD generalized Gabidulin codes are determined.