  This paper studies the existence and uniqueness of solution of It\^o type
stochastic differential equation $dx(t)=b(t, x(t), \om)dt+\si(t,x(t), \om) d
B(t)$, where $B(t)$ is a fractional Brownian motion of Hurst parameter $H>1/2$
and $dB(t)$ is the It\^o differential defined by using Wick product or
divergence operator. The coefficients $b$ and $\si$ are random and can be
anticipative. Using the relationship between the It\^o type and pathwise
integrals we first write the equation as a stochastic differential equation
involving pathwise integral plus a Malliavin derivative term. To handle this
Malliavin derivative term the equation is then further reduced to a system of
(two) equations without Malliavin derivative. The reduced system of equations
are solved by a careful analysis of Picard iteration, with a new technique to
replace the Gr\"onwall lemma which is no longer applicable. The solution of
this system of equations is then applied to solve the original It\^o type
stochastic differential equation up to a positive random time. In the special
linear and quasilinear cases the global solutions are proved to exist uniquely.
