Soils near the ground surface are naturally subjected to drying and wetting cycles because of climatic changes. The shear strength variations of soils induced by drying and wetting affect the stability of the geotechnical structures. The general objective of this study is to assess the effect of drying and wetting on the shear strength of a low-plasticity clay, classified as CL according to the Unified Soil Classification System, from Dalian, China. A series of consolidated undrained triaxial tests were conducted on the specimens with three different initial dry densities of 1.61, 1.71, and 1.76 Mg/m3. These tests were conducted under the saturated condition after the specimens were subjected to different numbers of drying and wetting cycles. The results indicate that drying and wetting have different impacts on the mechanical behaviors of soils with different initial dry densities. For the specimens with the initial dry density of 1.61 Mg/m3, the internal friction angle increased, whereas the residual strength and cohesion decreased after cyclic drying and wetting. The stress–strain relationships altered from strain hardening to strain softening. As for the specimens with the initial dry density of 1.71 and 1.76 Mg/m3, the internal friction angle, residual strength, and cohesion all decreased after cyclic drying and wetting. Based on the experimental results, it is concluded that the variations of the shear strengths can be attributed to the irreversible volume compression and the variation of dilatancy. The overall influence of drying and wetting on the mechanical behaviors depends on the initial state of soils.