  The Schr\"{o}dinger equation in three dimensional space with constant
positive curvature is studied for the Mie potential. Using analytic polynomial
solutions, we have obtained whole spectrum of the corresponding system. With
the aid of factorization method, ladder operators are obtained within the
variable and function transformations. Using ladder operators, we have given
the generators of $so(2,1)$ algebra and the Casimir operator which are related
to the Mie Oscillator on the positive curvature.
