In this paper the authors investigate the Moran sets which are defined by geometric fashion that distinguishes the classical self-similar sets from the following points: (i) the placements of the basic sets at each step of the constructions can be arbitrary; (ii) the contraction ratios may be different at each step; (iii) the lower limit of the contraction ratios permits zero. They determine the Hausdorff, packing and upper box-counting dimensions of the Moran sets by net and net measure techniques.