Starting with a manifestly conformal (O(d, 2) invariant) mechanics model in d space and 2 time dimensions, we derive the action for a massless spinning particle in d-dimensional anti-de Sitter space. The action obtained possesses both gauge N -extended worldline supersymmetry and local O(N ) invarince. Thus we improve the old statement by Howe et al. that the spinning particle model with extended worldline supersymmetry admits only flat space-time background for N > 2 (spin greater one). The original (d + 2)-dimensional model is characterized by rather unusual property that the corresponding supersymmetry transformations do not commute with the conformal ones, in spite of the explicit O(d, 2) invariance of the action.