  We study the phase structure of hyperscaling violating black holes using
Lyapunov exponents. For describing hyperscaling violating system, we chose a
particular gravity model constructed from generalized Einstein-Maxwell-Dilaton
action which includes the Lifshitz cases in appropriate limit. We study the
relationship between Lyapunov exponents and black hole phase transitions
considering both the timelike and null geodesics. We observe that, the black
hole phase transiton properties are reflected in Lyapunov exponent where its
multiple branches correspond to the distinct phases of the black hole. The
discontinuos change of the Lyapunov exponent during the phase transition serve
as an order parameter with critical exponent $1/2$ near the critical point. Our
numerical study reveals that the correlation between the Lyapunov exponent and
black hole thermodynamic properties can be generalised beyond the AdS
spacetime. We find that it is independent of the hyperscaling violation
parameter as well as the Lifshitz exponent.
