We study, for all p > 0 the asymptotic behavior of Lp extremal polynomials with respect to the measure α = β + γ, α denotes a positive measure whose support is the unit circle Γ plus a denumerable set of mass points, which accumulate at Γ and satisfy Blaschke’s condition and β = βa + βs, βs the absolutely continuous part of the measure satisfies Szegő condition and βs the singular part. Our main result is the explicit strong asymptotic formulas for the Lp extremal polynomials.