A laser ablation multi-collector inductively coupled plasma-mass spectrometry (LA-MC-ICP-MS) method was developed to obtain precise and accurate Pb isotopic ratio measurements in low-Pb materials (< 10 μg g-1) using a combination of Faraday cups and ion counters (FC-IC). The low abundance 204Pb (~ 1.4%) was collected using an IC. A NBS 981 standard solution was used to cross-calculate the FC-IC gain and to investigate the signal response characteristics of the IC. A significant, continuous and linear decrease in the FC-IC gain was observed within 1 hr, but this drift could be corrected using the calibrator-sample-calibrator bracketing method. In addition, a non-linear response of the IC used in this study was observed and corrected by a non-linear correction algorithm, which was established by measuring a series of gravimetrically prepared NBS 981 standard solutions (NIST SRM 981). Compared with the conventional arrangement, the use of the newly designed X skimmer cone and Jet sample cone improved the signal intensities from Pb isotopes by a factor of 1.9. Compared with only Faraday cups, using a combination FC-IC array was found to enhance the measurement repeatability (RSD) of 20xPb/204Pb by approximately one order of magnitude when the 204Pb intensity was < 8 mV. Eight natural glasses and the NIST SRM 612 reference material glass (as a calibration material) were measured to evaluate the new protocol for Pb isotope determination. The analytical results were in agreement with the reference values within 2s measurement uncertainties. For MPI-DING ATHO-G (5.67 μg g-1 total Pb), KL2-G (2.07 μg g-1 total Pb) and ML3B-G (1.38 μg g-1 total Pb), the typical accuracies of 20xPb/204Pb were 0.09% of preferred values with precisions of < 0.33% (2RSD). The Pb isotope ratios in feldspars from granodiorite and within mafic microgranular enclaves (MMEs) from the Fangshan pluton, North China, were measured using the present method. The Pb isotopic compositions of feldspars from the whole host granodiorite show that that are radiogenic in the margin zone and gradually become less radiogenic. For the MMEs, the Pb isotopic compositions of feldspars are highly variable and overlap with those of the whole host granodiorite. For single-grain feldspar, the strong rim-core-rim variations of the Pb isotopic compositions and trace elements are interpreted to have been generated via magma mixing. These results suggest that the Fangshan pluton underwent magma mixing of mantle-derived mafic magmas with felsic magmas, and the proportion of the mafic magma influx decreased over time.