General non-standard $tbW$ couplings are studied as model independently as possible based on the effective Lagrangian consisting of the dimension-6 operators, which is an extension of the standard-model Lagrangian. The $tbW$-interaction Lagrangian in this framework includes four kinds of couplings, which could be complex. Constraints on those non-standard $tbW$ couplings are obtained by comparing the experimental data related to the $t\to b W$ process with the corresponding theoretical formulas derived from the effective Lagrangian. The constraints on some sets of the non-standard couplings are shown not to be so strong because those couplings balance out each other as we treat all the non-standard couplings as complex numbers at the same time.