This work studies the influence of slice permutations on tensor recovery, which is derived from a reasonable assumption about algorithm, i.e. changing data order should not affect the effectiveness of the algorithm. However, as we will discussed in this paper, this assumption is not satisfied by tensor recovery under some cases. We call this interesting problem as Slice Permutations Variability (SPV) in tensor recovery. In this paper, we discuss SPV of several key tensor recovery problems theoretically and experimentally. The obtained results show that there is a huge gap between results by tensor recovery using tensor with different slices sequences. To overcome SPV in tensor recovery, we develop a novel tensor recovery algorithm by Minimum Hamiltonian Circle for SPV (TRSPV) which exploits a low dimensional subspace structures within data tensor more exactly. To the best of our knowledge, this is the first work to discuss and effectively solve the SPV problem in tensor recovery. The experimental results demonstrate the effectiveness of the proposed algorithm in eliminating SPV in tensor recovery.