The volume of the human left ventricular (LV) chamber is an important indicator for diagnosing heart disease. Although LV volume can be measured manually with cardiac magnetic resonance imaging (MRI), the process is difficult and time-consuming for experienced cardiologists. This paper presents an end-to-end segmentation-free method that estimates LV volume from MRI images directly. The method initially uses Fourier transform and a regression filter to calculate the region of interest that contains the LV chambers. Then convolutional neural networks are trained to estimate the end-diastolic volume (EDV) and end-systolic volume (ESV). The resulting models accurately estimate the EDV and ESV with a mean absolute error of 15.83 and 9.82 mL, respectively, and an ejection fraction with root mean square error of 5.56%. The comparison results show that the direct estimation methods possess attractive advantages over the previous segmentation-based estimation methods.