The conformation of a telechelic chain, such as ssDNA with complementary bases at both ends, fluctuates from loop (closed) to coil (open) state. The transition between open and closed states can be successfully described by the two-state model. However, the mismatch between one end with complementary bases in the central region along the chain complicates the transition. We investigate the kinetics of conformational fluctuations for an associating polymer of chain length N with an attractive site at both ends (α and β) and another attractive site in the midpoint (γ) by Monte Carlo simulations. The binding energy of α with β and γ is -ε1 and -ε2, respectively. The probability of the coil state, which varies with temperature and corresponds to the melting curve in experiments, is obtained. A three-state model including open (o), closed (c), and mismatch (m) states is proposed and agrees quite well with the simulation results. It is interesting that direct transition between mismatch and closed states is observed significantly at low enough temperature. The rate constants ki,j from i to j state are determined as well. ko,m, ko,c, and km,c are found to be independent of temperature but proportional to N-2. On the contrary, km,o and kc,o are independent of chain length but proportional to e-ε2/kBT and e-ε1/kBT, respectively. Nevertheless, the transition from closed to mismatch states kc,m follows N-2e-(ε1-ε2)/kBT For a long enough chain with ε1 > ε2, the two-state model is adequate since the mismatch state becomes insignificant.