This paper studies the finite-time synchronization for coupled neural networks with jumping inner coupling and non-fragile controller. A hidden-Markov observation model that covers many relevant Markovian jumping cases is applied to describe a more general situation where the synchronization controller has limited capability and partial modes observations. In terms of the hidden-Markov observations, a sufficient condition on the finite-time synchronization boundness is firstly derived by constructing a mode-dependent Lyapunov function for the augmented synchronization error system. Then an LMI framework is proposed for designing non-fragile synchronization controller gains. Finally, the effectiveness and the validity are demonstrated by a numerical example.