Disclosed are methods for establishing random access channel (RACH) transmission to prepare against the frequency offset. One of the methods reduces the length of the RACH preamble even if the frequency offset exists, allows the RACH preamble to include a repeated structure (also called an iterative structure) or to use a specific sequence with less affect on the frequency offset, so that the Node-B can easily detect the RACH preamble. If different conditions are established in a high-speed user equipment (UE) and a low-speed UE, an amount of system overheads can be reduced as compared to another case in which an overall RACH condition has been prescribed for only the high-speed UE irrespective of the low- speed UE. And, the method determines whether the UE can estimate its speed according to the aforementioned RACH setup condition, and prescribes a detailed RACH access method according to the determined result.