This paper proposes a new sequential weighted least squares (SWLS) method for positron emission tomography (PET) reconstruction. The SWLS algorithm is noniterative and can be considered as equivalent to the penalized WLS (PWLS) method under certain initial conditions. However, a full implementation of SWLS is computationally intensive. To overcome this problem, we propose a simplified SWLS as a reasonable alternative to the SWLS. The performance of this SWLS method is evaluated in experiments using both simulated and clinical data. The results show that the method can be advantageously compared with the original SWLS both in computation time and reconstruction quality.