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The Neimark-Sacker-pitchfork bifurcation can only occurs in the symmetric dynamic systems.A three-degree-of-freedom vibro-impact system with symmetry is considered.Due to the symmetry,the Poincaré map P is the second iteration of another virtual implicit map Q.The Neimark-Saker-pitchfork bifurcation of the symmetric fixed point of the Poincaré map P corresponds to the Neimark-Saker-flip bifurcation of the map Q.By using the map Q,according to the two-parameter unfolding of the normal form,we reveal the possible local dynamical behaviors of the symmetric fixed point of the Poincaré map P near the Neimark-Saker-pitchfork bifurcation point in detail.The numerical simulation represents the complicated local bifurcations near the Neimark-Saker-pitchfork bifurcation point.It is shown that with the symmetry action,when the Neimark-Saker-pitchfork bifurcation takes place,the symmetric fixed point will bifurcate into a single symmetric quasi-periodic attractor.