  The cosmic distance duality relation (CDDR), expressed as DL(z) = (1 +
z)2DA(z), plays an important role in modern cosmology. In this paper, we
propose a new method of testing CDDR using strongly lensed gravitational wave
(SLGW) signals. Under the geometric optics approximation, we calculate the
gravitational lens effects of two lens models, the point mass and singular
isothermal sphere. We use functions of {\eta}1(z) = 1 + {\eta}0z and {\eta}2(z)
= 1 + {\eta}0z=(1 + z) to parameterize the deviation of CDDR. By
reparameterizing the SLGW waveform with CDDR and the distance-redshift
relation, we include the deviation parameters {\eta}0 of CDDR as waveform
parameters. We evaluate the ability of this method by calculating the parameter
estimation of simulated SLGW signals from massive binary black holes. We apply
the Fisher information matrix and Markov Chain Monte Carlo methods to calculate
parameter estimation. We find that with only one SLGW signal, the measurement
precision of {\eta}0 can reach a considerable level of 0.5-1.3% for {\eta}1(z)
and 1.1-2.6% for {\eta}2(z), depending on the lens model and parameters.
