An expression for the Hamiltonian H(ρ1, ρ2, ρ3) of a vibrating-rotating triatomic molecule is derived using three curvilinear coordinates gi, Q 3 in such a way that the Hamiltonian obtained is applicable to any bent triatomic molecule and allows for large displacements in all the three modes of motion. A variational technique is then used to calculate the low lying vibrational energy levels (υ1, υ2, υ3) of the H2O molecule in its X̃1A1 ground state. The kinetic energy of the Hamiltonian T(ρ1, ρ2, ρ3) takes into account the large amplitude character of the three modes together with their interaction. But in order to minimize the formidable amount of computation, a simple quadratic potential F(ρ1, ρ2, ρ3) is assumed for all the three modes which only serves to illustrate the method of calculation.