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Orbital angular momentum(OAM),as a fundamental parameter of a photon,has attracted great attention in recent years.Although various properties and applications have been developed by modulating the OAM of photons,there is rare research about the non-uniform OAM.We propose and generate a new kind of contin-uously tunable azimuthally non-uniform OAM for the first time,to the best of our knowledge,which is carried by a hybridly polarized vector optical field with a cylindrically symmetric intensity profile and a complex polari-zation singularity.We also present the perfect vector optical field carrying non-uniform OAM with a fixed radius independent of topological charges,which can propagate steadily without radial separation,solving the problem of the unsteady propagation due to the broadened OAM spectrum of the non-uniform OAM.This new kind of tunable non-uniform OAM with a cylindrical symmetric intensity profile,complex polarization singularity,and propagation stability enriches the family of OAMs and can be widely used in many regions such as optical manipulation,quantum optics,and optical communications.