Neutrinos have been regarded as a unique tool for revealing the interiors of astronomical objects. KamLAND, which is a 1-kiloton liquid scintillator located in the Kamioka mine, detects electron antineutrinos through inverse beta decay. Due to its significant sensitivity in the energy region around a few MeV, KamLAND can detect supernova neutrinos (SN$\nu$s). To search for SN$\nu$s, we have performed a cluster event search and set an upper limit on the Galactic supernova rate. Neutrinos emitted a few hours before a supernova (pre-SN$\nu$) are also detectable. We have developed the combined alert system for pre-SN$\nu$s with the Super-Kamiokande group. In addition, we are developing a new background reduction scheme using a neural network to reduce atmospheric neutrino backgrounds in the supernova relic neutrino search. Other than SN$\nu$s, KamLAND has a sensitivity to neutrinos from primordial black holes, which are one of the candidates of dark matter. In this paper, we show the search progress of neutrinos from supernovae and primordial black holes.