This paper presents a blocked parallel implementation of a three-diagonal version of the Lattice Boltzmann Method. This method is a numerical model used to represent and to simulate fluid flows through mesoscopic approaches. Parallel implementations are often adopted to attend the demand of an expressive memory amount and processing power of the method. However, most implementations use simple data distribution strategies to parallelize the operations on the regular fluid data set. Fluid flows simulations crossing a cavity have been used as case study to evaluate our implementation. The presented results with blocked implementations achieve a performance 31% higher than non-blocked versions for some data distributions. Thus, this work shows that blocked implementations can be efficiently used to reduce the parallel execution time of the method.