In this paper, two types of failures including strength failure and stability failure of composite conical shells are studied by experiments and numerical simulations. Experiments of three composite conical shells with ply angles [40/90/90/40], [+/- 70/+/- 30], +/- 70/ +/- 30], and [+/- 45/+/- 45] +/- 45/ +/- 45] were performed. The corresponding failure processes and strain responses were obtained. Finite element (FE) models of the three different composite conical shells are built, and the corresponding stability failure and strength failure are analyzed, respectively. FE results and test results are compared, and it shows good agreement between them. In addition, the influence factors on the strength and stability of conical shells are considered: semi-cone angle, ply angle and stacking sequence, and thickness. Results reveal that with the increase of the semi-cone angle, both the critical buckling load and strength failure load decrease. The conical shell with stacking sequence of [90/+/- B/90] +/- B /90] has superior load-carrying characteristics than that with stacking sequence of [+/- B/+/- B]. +/- B / +/- B ]. When the thickness-radius ratio is less than 0.05, stability failure is the main failure type and when the thickness-radius ratio is larger than 0.08, strength failure is the main failure type.