  We investigate chiral and deconfinement transitions in the framework of the
strong coupling lattice QCD for color SU(3) with one species of unrooted
staggered fermion at finite temperature and quark chemical potential. We take
account of the leading order Polyakov loop terms as well as the
next-to-next-to-leading order (1/g^4) fermionic terms of the strong coupling
expansion in the effective action. We investigate the Polyakov loop effects by
comparing two approximation schemes, a Haar measure method (no fluctuation from
the mean field) and a Weiss mean-field method (with fluctuations). The
effective potential is obtained in both cases, and we analytically clarify the
Polyakov loop contributions to the effective potential. The Polyakov loop is
found to suppress the chiral condensate and to reduce the chiral transition
temperature at mu=0, and the chiral transition temperature roughly reproduces
the Monte Carlo results at beta=2N_c/g^2 \lesssim 4. The deconfinement
transition is found to be the crossover and first order for light (am_0
\lesssim 4 at beta=4) and heavy quark masses, respectively.
