When we throw a stone near an object floating on the surface of the water, we can see the water waves emerging in the water.
Now if we look at the object carefully it moves up and down and also it travels in the forward direction.
The up and down movement tells us about the transverse nature of the water wave and the object moving in the forward direction tells us about the longitudinal nature of the water wave.
So this suggests that a water wave is a combination of both Longitudinal and Transverse waves.
Hence, Water waves are both Transverse and Longitudinal.