Human induced pluripotent stem cells (hiPSCs), human embryonic stem cells (hESCs) and human umbilical cord MSCs (hUCMSCs) are exciting cell sources for use in regenerative medicine. There has been no report on long hydrogel fibers encapsulating stem cells inside injectable calcium phosphate cement (CPC) scaffold for bone tissue engineering. The objectives of this study were to: (1) develop a novel injectable CPC construct containing hydrogel fibers encapsulating cells for bone engineering, and (2) investigate and compare cell viability, proliferation and osteogenic differentiation of hiPSC-MSCs, hESC-MSCs and hUCMSCs in injectable CPC. The stem cell-encapsulating pastes were fully injectable under a small injection force, and the injection did not harm the cells, compared to cells without injection (p > 0.1). Mechanical properties of stem cell-CPC construct were much higher than previous injectable polymers and hydrogels for cell delivery. hiPSC-MSCs, hESC-MSCs and hUCMSCs in hydrogel fibers in CPC had excellent proliferation and osteogenic differentiation. All three cells yielded high alkaline phosphatase, runt-related transcription factor, collagen I, and osteocalcin expressions (mean ± sd; n = 6). Cell-synthesized minerals increased substantially with time (p < 0.05), with no significant difference among the three types of cells (p > 0.1). Mineralization by hiPSC-MSCs, hESC-MSCs and hUCMSCs in CPC at 14 d was 13-fold that at 1 d. In conclusion, all three types of cells (hiPSC-MSCs, hESC-MSCs and hUCMSCs) in CPC scaffold showed high potential for bone tissue engineering, and the novel injectable CPC construct with cell-encapsulating hydrogel fibers is promising to enhance bone regeneration in dental, craniofacial and orthopedic applications.