We present and analyse the kinematics and orbits for a sample of 488 open clusters (OCs) in the Galaxy. The velocity ellipsoid for our present sample is derived as (σ_U, σ_V, σ_W) = (28.7, 15.8, 11.0) km s⁻¹ which represents a young thin-disc population. We also confirm that the velocity dispersions increase with the age of a cluster subsample. The orbits of OCs are calculated with three Galactic gravitational potential models. The errors of orbital parameters are also calculated considering the intrinsic variation of the orbital parameters and the effects of observational uncertainties. The observational uncertainties dominate the errors of derived orbital parameters. The vertical motions of clusters calculated using different Galactic disc models are rather different. The observed radial metallicity gradient of clusters is derived with a slope of b=−0.070 � 0.011 dex kpc⁻¹. The radial metallicity gradient of clusters based on their apogalactic distances is also derived with a slope of b=−0.082 � 0.014 dex kpc⁻¹. The distribution of derived orbital eccentricities for OCs is very similar to that derived for the field population of dwarfs and giants in the thin disc.