The introduction of a random phase-shifting technique into a shadow moiré system, where an equal and known (or unknown) phase step is used to demodulate the phase of interest, is beneficial for the improvement of measurement accuracy. However, in spite of recent advances in optical metrology phase-shifting techniques, simultaneously estimating unequal and unknown phase shifts from three random phase-shifting fringe patterns remains a significant challenge. This paper presents a one-dimensional minimizer-based technique to address this ill-posed problem of phase demodulation from random phase-shifting patterns. In this method, two new sets of connected fringe patterns, without background illumination, are constructed through normalizing the secondary fringe patterns. Then, a generalized phase-shifting algorithm is developed by utilizing the character of the modulation factor's standard deviation distribution. Both numerical simulations and optical experiments are performed to demonstrate the high accuracy and robustness of the proposed method.