Abstract In a ( k , n ) visual cryptography scheme (VCS), a secret image is encoded into n shadow images that are distributed to n participants. Any k participants can reveal the secret image by stacking their shadow images, and less than k participants have no information about the secret image. In this paper we consider the case when the secret image is more than one, and this is a so-called multi-secret VCS (MVCS). The previous works on MVCS are all the simple 2-out-of-2 cases. In this paper, we discuss a general ( k , n )-MVCS for any k and n . This paper has three main contributions: (1) our scheme is the first general ( k , n )-MVCS, which can be applied on any k and n , (2) we give the formal security and contrast conditions of ( k , n )-MVCS and (3) we theoretically prove that the proposed ( k , n )-MVCS satisfies the security and contrast conditions.