Chitosan is a promising natural biomaterial for biological application; however, the weak mechanical performance of pristine chitosan limits its further utilization in hard tissue (such as cartilage) engineering. In this study, a chitosan-based 3D printing bioink with suitable mechanical properties was developed as 3D bioprinting ink for chondrocyte support. Chitosan was first modified by ethylenediaminetetraacetic acid (EDTA) to provide more carboxyl groups followed by physical crosslinking with calcium to increase the hydrogel strength. Dynamic mechanical analysis was carried out to evaluate viscoelastic properties with the addition of modified chitosan. A bioink with a combination of modified and pristine chitosan was formulated for scaffold fabrication via 3D bioprinting technique. Furthermore, cell viability, cell proliferation, and expression of chondrogenic markers were evaluated in vitro in chondrocytes loaded on the bioink. The novel bioink exhibited a favorable mechanical property and promoted cell attachment and chondrogenic gene expression in chondrocytes. Based on these results, we can conclude that the presented bioink could qualify for use in 3D bioprinting in cartilage tissue engineering.