In secret image sharing (SIS) scheme, a confidential image is en-crypted into multiple shadows, any group of shadows that reaches the thresh-old, otherwise nothing can be reconstructed at all. Most existing SIS schemes have a fixed threshold, however in this work, we consider more complicat-ed cases that the threshold may be adjusted due to the changeable security environment. In this paper, we construct a (k ↔ h, n) threshold changeable SIS (TCSIS) scheme using bivariate polynomial, which has h − k + 1 possible thresholds k, k + 1, ..., h. During image reconstruction, each participant can update the his shadow according to the current threshold T only based on his initial shadow. Comparing with previous TCSIS schemes, the proposed scheme achieves unconditional security, and can overcome the information disclosure problem caused by homomorphism.