In single photon emission computed tomography(SPECT), the non-stationary Poisson noise in the projection data is one of the major degrading factors that jeopardize the quality of reconstructed images. In our previous researches for low-dose CT reconstruction, based on the noise properties of the log-transformed projection data, a penalized weighted least-squares (PWLS) cost function was constructed and the ideal projection data(i.e., line integral) was then estimated by minimizing the PWLS cost function. The experimental results showed the method could effectively suppress the noise without noticeable sacrifice of the spatial resolution for both fan- and cone-beam low-dose CT reconstruction. In this work, we tried to extend the PWLS projection restoration method to SPECT by redefining the weight term in PWLS cost function, because the weight is proportional to measured photon counts for transmission tomography(i.e., CT) while inversely proportional to measured photon counts for emission tomography (i.e., SPECT and PET). The iterative Gauss-Seidel algorithm was then used to minimize the cost function, and since the weight term was updated in each iteration, we refer our implementation as penalized reweighted least-squares (PRWLS) approach. The restorated projection data was then reconstructed by an analytical cone-beam SPECT reconstruction algorithm with compensation for non-uniform attenuation. Both high and low level Poisson noise was simulated in the cone-beam SPECT projection data, and the reconstruction results showed feasibility and efficacy of our proposed method on SPECT.