TheLyot coronagraph is a widelyknown astronomical instrument used to realize direct imaging ofexoplanets, and
designing transmittance ofan apodizer and Lyot stop is the key to obtaining high-contrast imaging. In this paper, to the best ofour knowledge, a new optimization procedure used to design the apodizer and Lyot stop in the Lyot coronagraph is proposed. A two-step optimization program is established to obtain the optimum transmittance ofan apodizer and Lyot stop in a sequential way. By using the optimized apodizer and Lyot stop obtained through the proposed optimization procedure, both the stellar light and its diffraction light could be strongly suppressed. Numerical results indicate that such an optimized Lyot coronagraph can produce a 1e-10 extinction ofthe stellar light near the diffraction limit (1.59 λ/D), andahigh contrastimagingof1e-07 could still be obtained even with the influence oflight intensity ofplanets themselves. In addition, the two-step optimization procedure brings in two benefits. First, the two-step optimization is approximately 1000 times faster than the joint optimization method [Zimmerman et al. J. Astron. Telesc. Instrum. Syst. 2, 011012 (2016)]. Second, the optimum transmittance ofthe Lyot stop is binary, and therefore, the requirements of the production process are reduced, resulting in a greatly reduced cost. At the same time, the performance ofthe optimized Lyot coronagraph is also analyzed in the case ofa monochromatic light incident and bandwidth light incident, and the effect ofthe diameter ofthe Lyot stop on the results is also discussed in this paper, which makes sense when designing a coronagraph.