Lu-Hf geochronology is useful for constraining the evolution of geological systems. In this study, the in situ LA-ICP-MS/MS Lu-Hf dating technique was successfully applied to Paleozoic-Precambrian xenotime, apatite and garnet. For an iCap TQ ICP-MS/MS instrument (Thermo Fisher, USA), high-purity NH3 was more effective in the reaction than the commonly used 1 : 9 NH3-He mixture, and an 80% improvement in sensitivity was achieved using an N-2 flow rate of 4.0 mL min(-1). Lutetium, Yb and Hf reaction products with NH3 were identified in the mass range from 175-300 amu. The reaction product of Hf(176+82) (expressed for Hf-176((NH)-N-14-H-1)((NH2)-N-14-H-1)((NH3)-N-14-H-1)(3), mass shift by +82) is measured for the separation of Hf-176 from Lu-176 and Yb-176. Isobaric interferences Lu-176 and Yb-176 have extremely low reaction rates of similar to 0.0034% and similar to 0.00036% (at mass shift +82), which are only required to be corrected for the samples (e.g., xenotime) with extremely high Lu-175/Hf-177 and Yb-172/Hf-177 ratios. A matrix-induced bias of Lu-176/Hf-177 ratios was observed between NIST SRM 610 and the samples, which required further correction using matrix-matched reference materials. For xenotime, the accuracy of the common-Hf corrected single-spot ages is generally better than 1.5%, comparable to those obtained by in situ U-Pb analysis. The precisions of common-Hf corrected single-spot ages were in a range of 1.5-8.1% and 9.2-36.0% for xenotime and apatite samples. For garnet, the analytical uncertainties of the isochron ages are in a range of 3.5-10%, which could be further improved using a sensitivity-enhanced instrument and/or enlarged sampling volume. Our study revealed that the xenotime reference materials can be used as calibrators for apatite Lu-Hf dating. The novel in situ Lu-Hf dating technique may be especially useful for determining the age of the samples with complex temporal records or lack of traditional U-rich accessory minerals (e.g., zircon).