The authors study the class numbers of genera of \({\mathcal O}\)-lattices in a positive definite Hermitian space (V,H), the space being defined over an arbitrary imaginary quadratic field K with the ring of integers \({\mathcal O}\). Let \({\mathbb{G}}\) and \({\mathbb{G}}^{(1)}\) be the unitary group and the special unitary group of (V,H), respectively. For a \({\mathbb{G}}\)-genus \({\mathcal L}\) (resp. \({\mathbb{G}}^{(1)}\)-genus \({\mathcal L}^{(1)})\) of \({\mathcal O}\)-lattices in (V,H), denote by h(\({\mathcal L})\) (resp. \(h^{(1)}({\mathcal L}^{(1)}))\) the class number of \({\mathcal L}\) (resp. \({\mathcal L}^{(1)})\) with respect to \({\mathbb{G}}\) (resp. \({\mathbb{G}}^{(1)})\). In {\S} 2 the authors show, under some assumptions on K and \({\mathcal L}\), that \[ h({\mathcal L})=(h_ K/2^{t-1})\cdot h^{(1)}({\mathcal L}^{(1)})\quad for\quad any\quad {\mathcal L}^{(1)}\subset {\mathcal L} \] where \(h_ K\) is the class number of K and t is the number of distinct prime divisors of the discriminant of K (Theorem 2.9). In {\S} 3 the authors give a closed expression for h(\({\mathcal L})\) and \(h^{(1)}({\mathcal L}^{(1)})\) (Theorem 3.2), which expression is a special case of the trace formula for the Brandt matrices given by the first author [J. Fac. Sci., Univ. Tokyo, Sect. I A 27, 227-245 (1980; Zbl 0433.10017)]. The conjugacy classes of \({\mathbb{G}}_{{\mathbb{Q}}}\) are parametrized in {\S} 4, and the masses of the principal genera are calculated in {\S} 5. Using the latter the authors give a lower and an upper estimate for the class number (Theorem 5.11). The results in {\S}{\S} 3,4,5 and the results on unimodular Hermitian lattices in {\S} 6 are used in the authors' subsequent paper on the explicit formula for the class numbers [Tôhoku Math. J., II. Ser. 41, 171-216 (1989; Zbl 0668.10030, see the following review)].