We report bulk superconductivity induced by an isovalent doping of phosphorus in BaFe 2 (As 1− x P x) 2. The P-for-As substitution results in shrinkage of the lattice, especially for the FeAs block layers. The resistivity anomaly associated with the spin-density-wave (SDW) transition in the undoped compound is gradually suppressed by the P doping. Superconductivity with a maximum T c of 30 K emerges at x= 0.32, coinciding with a magnetic quantum critical point (QCP) which is shown by the disappearance of SDW order and the linear temperature-dependent resistivity in the normal state. The T c values were found to decrease with further P doping and no superconductivity was observed down to 2 K for x≥ 0.77. The appearance of superconductivity in the vicinity of QCP hints at the superconductivity mechanism in iron-based arsenides.