We present a novel and effective learning-based frame rate upconversion (FRUC) scheme, using linear mapping. The proposed learning-based FRUC scheme consists of: 1) a new hierarchical extended bilateral motion estimation (HEBME) method; 2) a light-weight motion deblur (LWMD) method; and 3) a synthesis-based motion-compensated frame interpolation (S-MCFI) method. First, the HEBME method considerably enhances the accuracy of the motion estimation (ME), which can lead to a significant improvement of the FRUC performance. The proposed HEBME method consists of two ME pyramids with a three-layered hierarchy, where the motion vectors (MVs) are searched in a coarse-to-fine manner via each pyramid. The found MVs are further refined in an enhanced resolution of four times by jointly combining the MVs from the two pyramids. The HEBME method employs a new elaborate matching criterion for precise ME which effectively combines a bilateral absolute difference, an edge variance, pixel variances, and an MV difference among two consecutive blocks and its neighboring blocks. Second, the LWMD method uses the MVs found by the HEBME method and removes the small motion blurs in original frames via transformations by linear mapping. Third, the S-MCFI method finally generates interpolated frames by applying linear mapping kernels for the deblurred original frames. In consequence, our FRUC scheme is capable of precisely generating interpolated frames based on the HEBME for accurate ME, the S-MCFI for elaborate frame interpolation, and the LWMD for contrast enhancement. The experimental results show that our FRUC significantly outperforms the state-of-the-art non-deep learning-based schemes with an average of 1.42 dB higher in the peak signal-to-noise-ratio and shows comparable performance with the state-of-the-art deep learning-based scheme.