The global distribution of the second lapse-rate tropopause (LRT2) is investigated with the radio occultation measurements from the constellation observing system for meteorology, ionosphere and climate (COSMIC) covering December 2006-November 2008 Comparisons between COSMIC and radiosonde in terms of the tropopause are examined in three stations to check the difference. The research results are as follows. 1) In the winter, occurrence frequency for LRT2 in the northern hemisphere (NH) is of 50%-70% and in the southers hemisphere is of 20%-40%. 2) The second tropopause over the equatorial zone with 20%-26% occurrence seems to be related to the equatorial jet stream and subvisual cirrus above the first tropopause. 3) In the tropic, the difference in altitude and occurrence between the first and second tropopause decrease with latitude. In the extratropic zone, the difference increases with latitude and reaches a maximum of 7-8 km in the winter of the NH. 4) The second tropopause occurs frequently over the subtropical jet stream region, in which the first tropopause temperature is almost higher than the second one. 5) The more intense the single station daily variations of tropopause height, the bigger the difference between COSMIC and radiosonde is.