The aim of this paper is to clear up the problem of the connection between the 3D geometric moments invariants and the invariant theory, considering a problem of describing of the 3D geometric moments invariants as a problem of the classical invariant theory.Using the remarkable fact that the complex groups $SO(3,\mathbb{C})$ and $SL(2,\mathbb{C})$ are locally isomorphic, we reduced the problem of deriving 3D geometric moments invariants to the well-known problem of the classical invariant theory.
 We give a precise statement of the 3D geometric invariant moments computation, intro\-ducing the notions of the algebras of simultaneous 3D geometric moment invariants, and prove that they are isomorphic to the algebras of joint $SL(2,\mathbb{C})$-invariants of several binary forms. To simplify the calculating of the invariants we proceed from an action of Lie group $SO(3,\mathbb{C})$ to equivalent action of the complex Lie algebra $\mathfrak{sl}_2$. The author hopes that the results will be useful to the researchers in thefields of image analysis and pattern recognition.