Different bioprinting techniques have been used to produce cell-laden alginate hydrogel structures, however these approaches have been limited to 2D or simple three-dimension (3D) structures. In this study, a new extrusion based bioprinting technique was developed to produce more complex alginate hydrogel structures. This was achieved by dividing the alginate hydrogel cross-linking process into three stages: primary calcium ion cross-linking for printability of the gel, secondary calcium cross-linking for rigidity of the alginate hydrogel immediately after printing and tertiary barium ion cross-linking for long-term stability of the alginate hydrogel in culture medium. Simple 3D structures including tubes were first printed to ensure the feasibility of the bioprinting technique and then complex 3D structures such as branched vascular structures were successfully printed. The static stiffness of the alginate hydrogel after printing was 20.18 ± 1.62 KPa which was rigid enough to sustain the integrity of the complex 3D alginate hydrogel structure during the printing. The addition of 60 mM barium chloride was found to significantly extend the stability of the cross-linked alginate hydrogel from 3 d to beyond 11 d without compromising the cellular viability. The results based on cell bioprinting suggested that viability of U87-MG cells was 93 ± 0.9% immediately after bioprinting and cell viability maintained above 88% ± 4.3% in the alginate hydrogel over the period of 11 d.