Topological tailoring of materials at a micro-scale can achieve a diverse range of extreme physical and mechanical properties. Modification of material properties through customizing the structural pattern paves an avenue for novel functional product design. In this paper, a non-periodic microstructure design framework is explored for functional parts design with high-strength and functional property gradation. To address the common problem of geometric frustration in non-periodic microstructure design, we employ a smooth transition layer to connect distinct structural patterns and thus achieve functional gradation between adjacent microstructures. The concept of spatial control points is introduced for implementing the transition layer. To pursue a superior macro-structural performance for designing objects, we formulate the control point as design variables and encapsulate it into macro-structural design optimization problems. Given that our objective function involves finite element (FE) simulations, a surrogate model-based optimization scheme is utilized to cope with the computational challenge brought by the FE simulation. Experimental results demonstrate that the proposed design framework can yield both functionally graded light-weight structures and high-strength macro-mechanical performance. The compatibility issues in traditional non-periodic microstructure design are addressed. Comparative studies reveal that the proposed framework is robust and can potentially generate desired functional products with spatially varying properties.