  We study the stability of circular orbits in the background of a traversable
wormhole (TWH) spacetime obtained as a solution of Einstein's field equations
coupled conformally to a massless scalar field. The Lyapunov stability approach
is employed to determine the stability of circular orbits (timelike and null)
of non-spinning test particles around a TWH spacetime. In the case of timelike
geodesics, the particle is confined to move in four different types of
effective potentials depending on various values of the angular momentum L with
both centrifugal and gravitational part. The effective potential for null
geodesics consists of only a centrifugal part. Further, we characterize each
fixed point according to its Lyapunov stability, and thus classify the circular
orbits at the fixed point into stable center and unstable saddle points by
depicting the corresponding phase-portraits.
