Underwriter need to participate in the process of new issue firms going public. Related reference about Taiwan's underwriter IPOs market share haven't appear. In this study, we expect to find out the relationship between Taiwan's underwriter IPOs market share and some related factors. Then offer issuer, underwriter and investor the conclusion as reference. The IPOs samples are selected during the period 1991 through 2000 in Taiwan. There are 475 newly issued firms in this period. We subtract some incomplete data samples and bank samples.There are 247 IPOs samples in our regression model. Although underwriter IPOs market share is less significantly impacted by IPOs offer price , results imply that when offer price is too low,this would damage issuer's benefit and lead to underwriter IPOs market share decrease. When offer price is too high, this would damage investor's benefit and just lightly lead to underwriter IPOs market share decrease. Results show that there is no industry specialization in Taiwan's underwriter industry. Although underwriter IPOs market share is less significantly impacted by IPOs one year performance,results imply that when underwriter market higher one year return IPOs, this would attract more investors and lead to underwriter IPOs market share increase.Results show that underwriter IPOs market share is significantly impacted by nderwriter's asset and age. The underwriter with larger asset and larger age gains more IPOs market share.