Abstract: In contrast to ab initio methods like first principles that handle small-scale systems, a multiband k?p method is more efficient for modeling low dimensional systems with a big compilation of atoms like quantum dots (QDs). Electronic structures are obtained only at low k but sufficient for simulating optoelectronic properties. The Fourier transform-based k?p method formulates both Hamiltonian matrix and envelope functions and thus solves the k?p equations in momentum space. Mathematically it linearizes differential equations and thus eliminates the demand for 3D-space meshing. Advantage on controlling spurious solutions due to its inborn cut-off process has been demonstrated, whereas incorporation of Burt-Foreman operator ordering further enhances such merit. Such a meshless process favors investigation with structural parameter variation, as demonstrated in our study on the truncated pyramidal QDs by varying the truncation factor. Funding support: National Natural Science Foundation of China (grant no. 61176085 61377055); the Department of Education of Guangdong Province, China (grant no. gjhz1103).