Cell-cycle associated promoter motif prediction is very important to understand the cell-cycle control and process. Modeling genome-wide gene expression as a function of the promoter sequence motif features has drawn great attention recently. The proposed techniques using this approach are not specific to cell-cycle associated motif discovery, hence find aperiodic motif weights across the time-course and lower sensitivity. Motifs are scored based on the successive model error reduction steps which may not reveal all relevant motifs since they are alternatives for the model. Another, drawback is, these methods output a list of sequences which may either contain several instances of a dominating motif box (a set of alternative sequence motifs) such as MCB or only a few instances of an important box. To address the above problems, we propose a multi-step constrained optimization based position weight matrix (PWM) motif finding methodology called ConstrainedMotif. It models the cell-cycle regulated gene expression as a linear function of the motif features while the weights of them are constrained to be periodic across the time-course. The score of a motif is the error reduction in the prediction by that motif alone. The multi-step modeling starts with a set of sequences and output a ranked list of cell-cycle associated PWM motifs. We evaluate this methodology using S. Cerevesiae cell-cycle data published by Spellman et al. The results show that ConstrainedMotif is more sensitive and most of the instances of the boxes are represented by the respective matching PWMs.