Superconductivity arises from two distinct quantum phenomena: electron pairing and long-range phase coherence. In conventional superconductors, the two quantum phenomena generally take place simultaneously, while in the underdoped high- T_{c} cuprate superconductors, the electron pairing occurs at higher temperature than the long-range phase coherence. Recently, whether electron pairing is also prior to long-range phase coherence in single-layer FeSe film on SrTiO_{3} substrate is under debate. Here, by measuring Knight shift and nuclear spin-lattice relaxation rate, we unambiguously reveal a pseudogap behavior below T_{p}∼60 K in two kinds of layered FeSe-based superconductors with quasi2D nature. In the pseudogap regime, a weak diamagnetic signal and a remarkable Nernst effect are also observed, which indicates that the observed pseudogap behavior is related to superconducting fluctuations. These works confirm that strong phase fluctuation is an important character in the 2D iron-based superconductors as widely observed in high-T_{c} cuprate superconductors.