Filter Bank Multi-Carrier (FBMC), has been proposed to solve the problems of spectral efficiency and adjacent channel leakage power in OFDM. This solution has added implications for the Peak-to-Average Power Ratio (PAPR) problem. This paper aims to reduce PAPR in FBMC through convolutional constellation mapping. The idea is to give a different constellation point to the symbol if successive values of the same symbol occur in the state space, thus reducing the chances of coherent addition of subcarriers without increasing the constellation points or even the need for iterative mapping. Computer-based simulations show the superior performance of the proposed Convolutional Constellation Mapping (CCM) in reducing the PAPR of FBMC.