In this paper an extensive study of the spectral response of the Fibonacci like Bragg gratings, that consist of multiple phase shifts, is presented. Namely in the presented analysis, for a grating with given physical parameters, a periodical structure is divided into N sections of constant length. For each section it is assumed that number of phase shifts is both distributed uniformly, and the index of section corresponds to the number of phase shifts in such a way, that for each next section number of phase shifts grows in accordance to the Fibonacci sequence. Both, symmetrical and asymmetrical structures are analyzed. For purpose of this analysis, a Coupled Mode Theory (CMT) together with Transfer Matrix Method (TMM) is employed.