Calcium-aluminum-rich inclusions (CAIs) in chondrite meteorites are the oldest rocks in the Solar System and were formed by condensation from nebular gas. Recent mass spectrometric measurements have revealed that CAIs possess nucleosynthetic isotopic compositions different from those of terrestrial materials for various elements, indicating a heterogeneous distribution of nuclides from various stellar sources in the early Solar System. CAIs are classified into coarse-grained (CGs) and fine-grained (FGs) inclusions. The former have experienced secondary melting through thermal events after their formation, while the latter evidently avoided the remelting. Thus, FGs are considered to be direct condensates from a high-temperature gas, making them ideal for the investigation of the origin and formation process of CAIs. In this study, the elemental abundances and Sr isotopic compositions in eight FGs from a carbonaceous chondrite Allende were analyzed by utilizing a micromilling technique. These FG samples were found to have rare-earth element (REE) patterns reflecting various degrees of elemental fractionation and variable µ84Sr values ranging from 61 to 844 ppm. It cannot be ruled out that matrix contamination during micromilling or secondary alteration on the Allende parent body has affected the elemental abundances and µ84Sr values observed in FGs to some extent; however, the large variation in µ84Sr values could reflect the variability in the FG formation processes. Importantly, REE-fractionated FGs, which were depleted in heavy REEs relative to light REEs, had relatively high µ84Sr values. This suggests that the formation of REE-fractionated FGs was triggered by rapid heating events, such as FU Orionis that occurred periodically in the early Solar System, and that at least two different heating events probably formed FGs with two different µ84Sr values.