Computing the high power of huge-dimension square matrix is a hard job for those entities (clients) with limited compute capability. To resolve this problem, a secure and verifiable cloud computation outsourcing protocol of square matrix power was designed using the cloud computing platform. In the protocol, the client firstly constructed a random permutation and generated a secret key which included a non-singular square matrix and its inverse matrix by combining the permutation with the Kronecker function. Secondly, the original square matrix was encrypted with the secret key by the client, and then the encrypted matrix was sent to the cloud along with the original exponent. After completing the calculation of the encrypted square matrix power, the cloud returned the result to the client. The client decrypted the returned result with its own secret key and correspondingly compared the elements which were randomly chosen by the client with the correct values to verify the correctness of the result. Theoretical analysis shows that the protocol meets the requirements of outsourcing protocol well, including correctness, security, verifiability and high efficiency. Based on this protocol model, the simulation experiments were conducted in two aspects: dimension fixed exponent changing and exponent fixed dimension changing. Finally the experiment result indicates that, compared with completing the original job by client himself, the outsourcing computation can substantially reduce the time consumption of the client in both cases and get a desirable outsourcing performance which becomes better with the increase of dimension and exponent.