A uniaxial concrete constitutive model considering the bond-slip effect is proposed and its finite element analysis (FEA) implementation on a fiber section of a beam-column element is presented. The tension-stiffening, crack-closing, crack-opening, cyclic degradation of the tensile capacity of reinforced concrete are modeled, which reveals the significance of energy dissipation resulting from bond slip during crack opening and closing under cyclic loading. The model is based on a simplified mechanical concept in a smeared manner and verified through quasi-static test results of X-type slender RC columns. The FEA results using a common concrete model with no consideration of bond slip present significant pinching when predicting the hysteretic loop of slender columns, which is not consistent with the test results and underestimates the capacity of energy dissipation of cracking during cyclic load. The results obtained with the proposed model show good agreement with the test results, which can reflect the degradation of stiffness and strength as well as the energy dissipation of the crack opening and closing due to the bond slip effect. Considering its simplicity and computational efficiency, it is more applicable for analyzing large-scale structures than other methods that consider the bond-slip effect, especially for slender columns, such as those used in cooling towers and subjected to seismic excitation.