This work proposes a residual recurrent neural network (RRNet) for synthetically extracting spectral information and estimating stellar atmospheric parameters together with 15 chemical element abundances for medium-resolution spectra from the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST). The RRNet consists of two fundamental modules: a residual module and a recurrent module. The residual module extracts spectral features based on the longitudinally driving power from parameters, while the recurrent module recovers spectral information and restrains the negative influences from noises based on Cross-band Belief Enhancement. RRNet is trained by the spectra from common stars between LAMOST DR7 and the APOGEE-Payne catalog. The 17 stellar parameters and their uncertainties for 2.37 million medium-resolution spectra from LAMOST DR7 are predicted. For spectra with a signal-to-noise ratio >=10, the precision of estimations (Teff and logg) are 88K and 0.13dex, respectively, elements C, Mg, Al, Si, Ca, Fe, and Ni are 0.05-0.08dex, and N, O, S, K, Ti, Cr, and Mn are 0.09-0.14dex, while that of Cu is 0.19dex. Compared with StarNet and SPCANet, RRNet shows higher accuracy and robustness. In comparison to Apache Point Observatory Galactic Evolution Experiment and Galactic Archaeology with HERMES surveys, RRNet manifests good consistency within a reasonable range of bias.