Purpose: We investigate biases in the assessments of left ventricular function (LVF), by compressed sensing (CS)-cine magnetic resonance imaging (MRI). Materials and Methods: Cardiovascular cine images with short axis view, were obtained for 8 volunteers without CS. LVFs were assessed with subsampled data, with compression factors (CF) of 2, 3, 4, and 8. A semi-automatic segmentation program was used, for the assessment. The assessments by 3 CS methods (ITSC, FOCUSS, and view sharing (VS)), were compared to those without CS. Bland-Altman analysis and paired t-test were used, for comparison. In addition, real-time CS-cine imaging was also performed, with CF of 2, 3, 4, and 8 for the same volunteers. Assessments of LVF were similarly made, for CS data. A fixed compensation technique is suggested, to reduce the bias. Results: The assessment of LVF by CS-cine, includes bias and random noise. Bias appeared much larger than random noise. Median of end-diastolic volume (EDV) with CS-cine (ITSC or FOCUSS) appeared -1.4% to -7.1% smaller, compared to that of standard cine, depending on CF from (2 to 8). End-systolic volume (ESV) appeared +1.6% to +14.3% larger, stroke volume (SV), -2.4% to -16.4% smaller, and ejection fraction (EF), -1.1% to -9.2% smaller, with P < 0.05. Bias was reduced from -5.6% to -1.8% for EF, by compensation applied to real-time CS-cine (CF = 8). Conclusion: Loss of temporal resolution by adopting missing data from nearby cardiac frames, causes an underestimation for EDV, and an overestimation for ESV, resulting in underestimations for SV and EF. The bias is not random. Thus it should be removed or reduced for better diagnosis. A fixed compensation is suggested, to reduce bias in the assessment of LVF.