In 2009, Anderson and Thakur constructed certain power series such that Thakur's multiple zeta values (MZV's) appear as the constant terms of the Taylor series of these power series at some point. They are called t-motivic MZV's. By using them, Anderson and Thakur gave a period interpretation of Thakur's MZV's. In this talk, we study not only constant terms but also Taylor coefficients of higher degree terms of t-motivic MZV's. In particular, I give certain families of these coefficients such that they are algebraically independent over a base field.