Matching module plays a critical role in display advertising systems. Different from sponsored search where user intentions can be captured naturally through query, display advertising has no explicit information about user intentions. Thus, it is challenging for display advertising systems to match user traffic and ads suitably w.r.t. both user experience and advertising performance. From the advertiser's view, system packs up a group of users with common properties, such as the same gender or similar shopping interests, into a crowd. Here term crowd can be viewed as a tag over users in the same crowd. Then advertisers bid for different crowds and deliver their ads to those targeted users. From the advertising system's view, things turn to be a little different. So far as we know, matching module in most industrial display advertising systems follows a two-stage paradigm. When receiving a user visit request, matching system (i) finds the crowds that the user belongs to; (ii) retrieves all ads that have targeted those crowds. However, in real world applications, such as the display advertising at Alibaba, with volume of crowds reaching up to tens of millions and volume of ads reaching up to millions, both stages of matching have to truncate the long-tailed user-crowd or crowd-ad pairs for online serving, under limited latency and computation cost requirements. That is to say, not all advertisers that bid for a given user have the chance to participate in the online matching process. This results in sub-optimal advertising performance for advertisers. Besides, it also brings loss of revenue of the advertising platform.In this paper, we study carefully the truncation problem and propose a Truncation-Free Matching System (TFMS). The basic idea of TFMS is to decouple the matching computation from the online processing pipeline. Instead of executing the two-stage matching when user visits, TFMS utilizes a near-line truncation-free matching module to pre-calculate and store those top valuable ads for each user. Then, the online pipeline just needs to fetch the pre-stored candidate ads as the result of matching. In this way, near-line matching can jump out of the online system's latency and computation cost limitations and leverage flexible computation resources to finish the user-ad matching process. Moreover, we can employ arbitrary advanced models to conduct the top-n candidate selection in the near-line matching system over all candidate ad set, bringing superior performance compared with original roughly truncated online * Both authors contributed equally to this work. matching system. Since 2019, TFMS has been deployed in our productive display advertising system, bringing (i) more than 50% improvement of impressions for advertisers who encountered truncation before, (ii) 9.4% RPM (Revenue Per Mile) gain for advertising system, which is significant enough for the business.