Electrokinetic energy conversion being a promising clean energy production technology utilizes the electric double layer (EDL) in a nanochannel to convert hydrodynamic energy to electrical power. The previous research mainly focuses on the electrokinetic energy conversion in straight nanochannels. In this work, we perform a systematic investigation of electrokinetic energy conversion in a conical nanochannel. For this purpose, a multiphysical model consisting of the Planck-Nernst-Poisson equation and Navier-Stokes equation was formulated and solved numerically. Particularly, we discover various regulation effects in the electrokinetic energy conversion in conical nanochannels that the energy conversion characteristics (streaming potential, streaming current and I-V characteristics) are different for a forward pressure difference and a backward pressure difference of the same magnitude. These regulation effects are found to be caused by the conicity of channel. Then the effects of the channel conicity, applied pressure difference and the surface charge density on the performance of electrokinetic energy conversion are discussed in details. It is generally shown that the regulation effects are enhanced by increasing the conicity, pressure difference and surface charge density. The conclusions from this work can serve as important reference and guidelines for the design and operation of electrokinetic energy conversion devices.