This paper aims at constructing a six-component integrable hierarchy associated with a matrix spatial spectral problem with six potentials and three signs. The zero curvature formulation and the trace identity are used to generate integrable models and their Hamiltonian structures, respectively. Two expository examples of integrable models of lower orders are six-component integrable coupled nonlinear Schrödinger (NLS) equations and modified Korteweg–de Vries (mKdV) equations. The motivation of this study is to explore typical integrable coupled NLS equations and mKdV equations, and the innovative idea and main advance is to introduce a specific matrix spectral problem involving three signs to construct integrable coupled equations.