The lightest neutralino, as the dark matter candidate, can be gravitationally captured by the Sun. In this paper, we studied the high energy neutrino signals from solar neutralino annihilations in the core of the Sun in the anomaly mediated supersymmetry breaking (AMSB) model. Based on the event-by-event Monte Carlo simulation code WimpSim, we studied the detailed energy and angular spectrum of the final muons at large neutrino telescope IceCube. More precisely, we simulated the processes since the production of neutrino via neutralino annihilation in the core of the Sun, neutrino propagation from the Sun to the Earth, as well as the converting processes from neutrino to muon. Our results showed that in the AMSB model it is possible to observe the energetic muons at IceCube, provided that the lightest neutralino has a relatively large Higgsino component, as a rule of thumb ${N}_{13}^{2}+{N}_{14}^{2}>4%$, or equivalently, ${\ensuremath{\sigma}}_{\mathrm{SD}}>{10}^{\ensuremath{-}5}\text{ }\text{ }\mathrm{pb}$. Especially, for our favorable parameters the signal annual events can reach 102, and the statistical significance can reach more than 20. We pointed out that the energy spectrum of muons may be used to distinguish among the AMSB model and other supersymmetry breaking scenarios.