We present the anisotropic clustering of emission-line galaxies (ELGs) from the Sloan Digital Sky Survey IV (SDSS-IV) extended Baryon Oscillation Spectroscopic Survey (eBOSS) Data Release 16 (DR16). Our sample is composed of 173 736 ELGs covering an area of 1170 deg2 over the redshift range 0.6 <= z <= 1.1. We use the convolution Lagrangian perturbation theory in addition to the Gaussian streaming redshift space distortions to model the Legendre multipoles of the anisotropic correlation function. We show that the eBOSS ELG correlation function measurement is affected by the contribution of a radial integral constraint that needs to be modelled to avoid biased results. To mitigate the effect from unknown angular systematics, we adopt a modified correlation function estimator that cancels out the angular modes from the clustering. At the effective redshift, z(eff) = 0.85, including statistical and systematical uncertainties, we measure the linear growth rate of structure f sigma(8)(z(eff)) = 0.35 +/- 0.10, the Hubble distance D-H (z(eff))/r(drag) = 19.1(-2.1)(+1.9), and the comoving angular diameter distance D-M(z(eff))/r(drag) = 19.9 +/- 1.0. These results are in agreement with the Fourier space analysis, leading to consensus values of: f sigma(8)(z(eff)) = 0.315 +/- 0.095, D-H (z(eff))/r(drag) = 19.6(-2.1)(+2.2), and D-M(z(eff))/r(drag) = 19.5 +/- 1.0, consistent with Lambda CDM model predictions with Planck parameters.