A method of random access, a terminal device, and a non-transitory computer-storage medium are provided. The method includes the following. In response to a terminal device failing to achieve access when a value of a counter for recording a number of transmissions of a random access message containing a preamble reaches N during a first random access procedure, the terminal device switches from the first random access procedure to a second random access procedure, where the counter is further configured to count a number of transmissions of a random access message containing a preamble during the second random access procedure, and N is a positive integer.