In this paper, we present a novel image reconstruction method based on weighted least squares (WLS) objective function for positron emission tomography (PET). Unlike a usual WLS algorithm, the proposed method, which we call it SA-WLS, combines the SAGE algorithm with WLS algorithm. It minimized the WLS objective function using single coordinate descent (SCD) method in a sequence of small “hidden” data spaces (HDS). Although SA-WLS used a strategy to update parameter sequentially just like common SCD method, the use of these small HDS makes it converge much faster and produce the reconstructed images with greater contrast and detail than the usual WLS method. In order to decrease further the actual CPU time per iteration, the adaptive variable index sets were introduced to modify SA-WLS (MSA-WLS). Instead of optimizing each pixel, this MSA-WLS method sequentially optimizes many pixels located in an index set at one time. The index sets were automatically modified during each iteration step. MSA-WLS gathers the virtue of simultaneously and sequentially updating the parameters so that it achieves a good compromise between the convergence rate and the computational cost in PET reconstruction problem. Details of these algorithms were presented and the performances were evaluated by a simulated head phantom.