This study aims to understand immigrants` difficulty using Korean language in their core communication situation. Specifically, three research questions are explored. (a) In which communication situation (general or core) do immigrants feel more difficulty? (b) What are the significant factors affecting their difficulty in core communication situation? (c) How does the difficulty change according to their arrival-age and length-of-residence? A total of 482 subjects were divided into three groups(immigrant-woker (IW), marriage-immigrant (MI), and immigrant-child (IC)), and responded to the same survey questions used in Min et al.(2016): length-of-residence(R), length-of-learning(L), ability-of-Korean(A) and difficulty-of-Korean(D), as well as arrival age(S) and gender(G). Followings are the details of analysis: (a) Paired t-test shows that IW and IC feel more difficulty in core situation than general situation, whereas MI feels same level of difficulty in both situation. (b) Conditional Process Analysis(Hayes, 2013) shows that each of R(predictor), L(moderator), A(mediator), and S(covariance) has an effect on immigrants` difficulty in core situation. But MI`s final path model doesn`t have moderator and covariance. (c) If a 26.6-year-old IW arrives in Korea, his/her difficulty declines to the `normal` level after 3.7 years. If a 6.0-year-old IC arrive at Korea, his/her difficulty declines to the `not-difficult` level after 5.3 years. But MI`s difficulty declines to the `normal` level after 2.9 years, regardless of arrival-age. Based on these analysis, this study discusses the weak interpretation of critical period and the effectiveness of Korean language education for MI.