A search of neutrino magnetic moment was carried out at the Kuo-Sheng Nuclear Power Station at a distance of 28 m from the 2.9 GW reactor core. With a high purity germanium detector of mass 1.06 kg surrounded by scintillating NaI(Tl) and CsI(Tl) crystals as anti-Compton detectors, a detection threshold of 5 keV and a background level of 1 kg(-1) keV(-1) day(-1) at 12-60 keV were achieved. Based on 4712 and 1250 h of reactor ON and OFF data, respectively, the limit on the neutrino magnetic moment of mu(nu;(e))<1.3x10(-10)mu(B) at 90% confidence level was derived. An indirect bound of the nu;(e) radiative lifetime of m(3)(nu)tau(nu)>2.8x10(18) eV(3) s can be inferred.