The Gaussian-type orbital and Gaussian-type geminal (GGn) model is applied to the water molecule, at the level of second-order Møller-Plesset (MP2) theory. In GGn theory, correlation factors are attached to all doubly-occupied orbital pairs (GG0), to all doubly-occupied and singly-excited pairs (GG1), or to all orbital pairs (GG2). Optimizing the GG2 model using a weak-orthogonality functional, we obtain the current best estimate of the all-electron MP2 correlation energy of water, -361.95 mE(h). In agreement with previous observations, the GG1 model performs almost as well as the GG2 model (-361.26 mE(h)), whereas the GG0 model is poorer (-351.36 mE(h)). For the barrier to linearity of water, we obtain an MP2 correlation contribution of -463 +/- 5 cm(-1).