The solenoid lens is the only transverse focusing device in the ultrafast electron diffraction (UED) system that is being developed at HUST, which  control the beam spot size and compensate the beam transverse emittance. This paper focuses on the parameter optimization of the multi-coil solenoid lens MeV-UED to obtain a desired magnetic field,，especially for the shape of the pole shoe, the axial and radial dimensions of the solenoid. Two finite element analysis (FEA) software Opera and Parmela are combined to optimize the electromagnetic field. Results show that after parameter optimization, the transverse beam emittance can be reduced by 60.6%, and the beam spot size is reduced by 70%.
 

Ultrafast electron diffraction,solenoid lens,beam spot,beam transverse emittance,parameter optimization