In this study, the stability and flexibility of fiber perovskite resistive random-access memory (FP-RRAM) were optimized via a 3D urea-spherical dendritic framework, which was produced using amino-terminal PAMAM and toluene diisocyanate (TDI). Spherical dendritic PAMAM optimized the perovskite crystallization process in the precursor solution. Next, TDI was added to an anti-solvent to establish the 3D urea-spherical dendritic framework via strong covalent bonds. This covalently connected 3D framework was used as a crystallization template in this work to obtain a more uniform and smoother perovskite morphology. Meanwhile, the urea components protect the surface of the perovskite device, affording better stability and flexibility. When 2 mol L−1 PAMAM in the perovskite precursor solution and 10% TDI in the anti-solvent were applied, the RRAM device modified using the covalently constructed 3D framework (cf-RRAM) achieved optimal resistive switching (RS) performance with an ON/OFF ratio of 108, 500 cycles and a data retention time of 104 s. This optimized RS performance provides the potential to construct a woven and multi-storage device, implying high-density storage. In the exploration of cf-RRAM flexibility, the ON/OFF ratio of the perovskite film was still maintained when the elongation at break reached 28.91% or after bending 400 times at a radius of 5 mm. The loss of RS performance of cf-RRAM devices was less even under frictional conditions. In the exploration of cf-RRAM stability, the devices could withstand a high-temperature environment below 200 °C and maintained good RS performance after 90 day exposure to the ambient environment.