In the breakthrough progress made in the latest experiment Hou et al (2022 Nature 606 507), 2D C 60 polymer was exfoliated from the quasi-hexagonal bulk crystals. Bulk C 60 polymer with quasi-tetragonal phase was found to easily form 1D fullerene structure with C 60 molecules connected by C=C. Inspired by the experiment, we investigate the strain behaviors of 1D and 2D C 60 polymers by first-principles calculations. Some physical properties of these low dimensional C 60 polymers, including structural stability, elastic behavior, band alignment and carrier mobility, are predicted. Compared with fullerene C 60 molecule, 1D and 2D C 60 polymers are metastable. At absolute zero temperature, 1D C 60 bears a uniaxial tensile strain less than 11.5%, and 2D monolayer C 60 withstands a biaxial tensile strain less than 7.5%. At 300 K, ab initio molecular dynamics confirm that they can withstand the strains of 9% and 5%, respectively. Strain engineering can adjust the absolute position of the band edge. In the absence of strain, carrier mobility is predicted to be µ e = 398 and µ h = 322 c m 2 V − 1 s − 1 for 1D C 60 polymer, and μ e , x = 74 / μ e , y = 34 c m 2 V − 1 s − 1 and μ h , x = 646 / μ h , y = 1487 c m 2 V − 1 s − 1 for 2D C 60 polymer. Compared with other carbon based semiconductors, these C 60 polymers exhibit high effective mass, resulting in low mobility.