To study the stress mechanism of grouted sleeve lapping connectors for rebars with large diameters, a total of 36 lapping connectors were tested under uniaxial tensile load. The failure modes, bearing capacity, ductility, and sleeve strain of the connectors were investigated. Test results show that with the same relative lapping length, the yield strength and ultimate load of the specimens increased with the increase of the rebar diameter. Meanwhile, specimens with larger lapping lengths had better initial stiffness and ductility. At the early stage of loading, the sleeve was in longitudinal tensile state, and at the late loading stage, it was in longitudinal compression state. The conversion load of longitudinal sleeve strain from tension to compression increased gradually with increasing lapping length. With the increase of the lapping length, the longitudinal tensile strain of the sleeve near the rebar increased during the loading process, while the longitudinal compressive strain of the sleeve in the far side of the rebar decreased under ultimate load. At the early stage of the loading process, the circumferential strain in the middle of the sleeve was larger than that in the edge section. When the ultimate load was reached, the circumferential strain of the sleeve in the edge section was smaller than that in the middle section due to the shedding of the grout at the end of the specimens. The force transmission path and mechanical mechanism of the connectors were analyzed. The distribution and development of longitudinal sleeve stress were analyzed based on the curve of rebar-concrete bond stress, and results show that the sleeve was in longitudinal tensile state at the early stage of loading and in longitudinal compression state at the late loading stage, which was consistent with test results. The calculation formulas for the ultimate bond strength and critical lapping length of grouted sleeve lapping connectors were proposed based on the test data. The research lays theoretical foundations for the application of such connectors.