We have carried out tilt magnetic field (B) studies of the u=12/5 fractional quantum Hall state in an ultra-high quality GaAs quantum well specimen. Its diagonal magneto-resistance Rxx shows a non-monotonic dependence on tilt angle (theta). It first increases sharply with increasing theta, reaches a maximal value of ~ 70 ohms at theta ~ 14^o, and then decreases at higher tilt angles. Correlated with this dependence of Rxx on theta, the 12/5 activation energy (Delta_{12/5}) also shows a non-monotonic tilt dependence. Delta_{12/5} first decreases with increasing theta. Around theta = 14^{o}, Delta_{12/5} disappears as Rxx becomes non-activated. With further increasing tilt angles, Delta_{12/5} reemerges and increases with theta. This tilt B dependence at u=12/5 is strikingly different from that of the well-documented 5/2 state and calls for more investigations on the nature of its ground state.
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