For requriement of plasma diagnostic system in inertial confinement fusion (ICF) drivers, simple lens which can be substituted for logarithmic axicon is designed by nonlinear-phase fitting method. Required sperhical lens parameters are determined by fitting the phase of sperhical lens and logarithmic axicon. A long-focal-depth lens applied for plasma diagnostic system is designed, and the optical performance of lens is analyzed, such as long focal depth, homogeneous axial , transverse intensity distribution and side lobe of focal spot. Numerical results show that long-focal-depth lens has the same phase distribution with logarithmic axicon, its optical performance can satisfy the requirements of plasma diagnostic system, so the nonlinear phase fitting method is valid.