Cloud computing helps resource constraint customer to outsource their computations. This committed computing illustration inevitably brings in new privacy anxiety and contravention, just like input/output security and result verification. Constrained linear least-square (CLLS) is a quite common task in various scientific and engineering methods. This paper designs a tremendous protocol to make a secure, reliable and efficient outsourcing of CLLS to cloud. It applies some techniques to get an encrypted input for protecting privacy which will be sent to the cloud for computation. Both analytically and experimentally, it is proved that the proposed protocol fulfills the goals of cloud outsourcing like as security, result verifiability and efficiency.