In the near-IR, the sky background is dominated by highly variable air glow emission lines. This is an issue for the sky subtraction in spectra without plain sky, where reference sky spectra taken at a different time as the object spectrum are required. For this reason, we have developed the instrument-independent sky subtraction code SKYCORR, which uses physically motivated line group scaling in the reference sky spectrum by a fitting approach for an improved sky line removal in the object spectrum. Possible wavelength shifts between both spectra are corrected by fitting Chebyshev polynomials and advanced rebinning without resolution decrease. For the correction, the optimised sky line spectrum and the automatically separated sky continuum (without scaling) is subtracted from the input object spectrum. Tests show that SKYCORR performs well (percent level residuals) for data in different wavelength regimes and of different resolution, even in the cases of relatively long time lags between the object and the reference sky spectrum. Lower quality results are mainly restricted to wavelengths not dominated by airglow lines or pseudo continua by unresolved strong emission bands.