We considered the problem of accurately estimating the heart rate (HR) using photoplethysmography (PPG) signals that are contaminated by motion artifacts (MA). A novel HR estimation approach based on GRidless spectral Estimation and SVM-based peak Selection, denoted by GRESS, was proposed. It first obtained the sparse spectrum of PPG using a continuous dictionary, then a simple spectral subtraction step was adopted to remove MA, finally an SVM-based method was developed to select the spectral peak corresponding to HR. Experimental results on the PPG datasets used in 2015 IEEE Signal Processing Cup showed that the proposed approach had excellent performance.