As a research field of stream ciphers, the pursuit of a balance of security and practicality is the focus. The conditions for security usually have to satisfy at least high period and high linear complexity. Because the feedforward clock-controlled structure can provide quite a high period and utility, many sequence ciphers are constructed based on this structure. However, the past study of its linear complexity only works when the controlled sequence is an m-sequence. Using the theory of matrix over the ring and block matrix in this paper, we construct a more helpful method. It can estimate the lower bound of the linear complexity of the feedforward clock-controlled sequence. Even the controlled sequence has great linear complexity.