A new stream cipher design scheme is proposed, which uses the sequences generated by two chaotic systems to inter-perturb their sequence values and the control parameter, so as to obtain a new sequence as key stream. Inter-perturbed sequence and Logistic sequence are tested by several tests of NIST's (National Institute of Standards and Technology) STS randomness test suite. Simulation results prove that the cryptographical properties of inter-perturbation sequence are better than those of Logistic sequence. k-error approximate entropy is proposed to test the stability of inter-perturbed sequence and Logistic sequence. Simulations indicate that the stability of inter-perturbed sequence is better than that of Logistic sequence. An image is encrypted and decrypted by the inter-perturbed sequence. Simulation results show that the inter-perturbation sequence can cover up plaintext effectively and safely.