Message passing model, represented by MPI (Message Passing Interface), is the principal parallel programming tool for distributed computer systems. The most of MPI-programs contain collective communications, which involve all the processes of a parallel program. Effectiveness of collective communications substantially effects on total time of program execution. In this work, we consider the problem of design of adaptive algorithms of collective communications on the example of barrier synchronization, which refers to one of the most common types of collective communications. We developed adaptive algorithm of barrier synchronization, which suboptimally selects barrier synchronization scheme in parallel MPI-programs among such algorithms as Central Counter, Combining Tree and Dissemination Barrier. The adaptive algorithm chooses the barrier algorithm with the minimal evaluation of execution time in the model LogP. Model LogP considers performance of computational resources and interconnect for point-to-point communications. Proposed algorithm has been implemented for MPI. We present the results of experiments on cluster systems, analyse dependency of algorithm selection on LogP parameters values. In particular, for the number of processes less than 20 adaptive algorithm selects Combining Tree, while for a larger number of processes adaptive algorithm selects Dissemination Barrier. Developed algorithm minimizes average time of barrier synchronization by 4%, in comparison with the most common determined barrier algorithms.