A general geometric model of the elliptical cross-section double-ogive-nose projectile (ECDP) was established, and the expression of penetration resistance was obtained. Based on the special shape and penetration process characteristics of the ECDP, a three-stage penetration model was constructed, and closed-form penetration equations were derived. Three ECDPs with the major-minor axis ratio of 1.5 were launched by a 130 mm gas-gun to impact the plain concrete targets with the oblique angle of 10° at a nominal striking velocity of 650 m/s, the experimental data such as the penetration depth of the ECDPs and the failure characteristic parameter of the targets was obtained. The initial posture of the ECDP had little effect on the penetration depth and trajectory deflection under the condition of the target with 10° oblique angle, but it had obvious influence on the structural response. The theoretical model was verified by experimental data, the calculated result of the penetration depth was in good agreement with the experimental data, the deviation was within the range of -13.5% ~ -8.5%.