<p>Monte Carlo Markov chain (MCMC) samplings can obtain a set of samples by directed random walk, mapping the posterior probability density of the model parameters in Bayesian framework. We perform earthquake waveform inversion to retrieve focal angles or the elements of moment tensor and source location using a Bayesian MCMC method with the constraints of first-motion polarities and double couple percentage using full Green functions and data covariance matrix. The algorithm tests the compatibility with polarities and also checks the double couple percentage of every site before the time-consuming synthetic seismogram computation for every sample of moment tensor of every trial source position. Other than large earthquakes, the method is especially suitable for weak events (M < 4) that their focal mechanisms cannot be well-constrained by polarities or seismograms alone, unless a dense local network is available; something that is generally occasional. Two- and one-station solutions show more agreement with all-station solution if polarity and DC % constraints are employed. In order to examine the validity of the method, two events with the independent focal mechanism solutions are utilized. Furthermore, we also calculate data covariance matrix from pre-event noise and Green function uncertainty to obtain the errors of focal mechanisms.</p>