  In this paper, we study all possible orders which are less than 1 of
transcendental entire solutions of linear difference equations
  \begin{equation}
  P_m(z)\Delta^mf(z)+\cdots+P_1(z)\Delta f(z)+P_0(z)f(z)=0,\tag{+}
  \end{equation} where $P_j(z)$ are polynomials for $j=0,\ldots,m$. Firstly, we
give the condition on existence of transcendental entire solutions of order
less than 1 of difference equations (+). Secondly, we give a list of all
possible orders which are less than 1 of transcendental entire solutions of
difference equations (+). Moreover, the maximum number of distinct orders which
are less than 1 of transcendental entire solutions of difference equations (+)
are shown. In addition, for any given rational number $0<\rho<1$, we can
construct a linear difference equation with polynomial coefficients which has a
transcendental entire solution of order $\rho$. At least, some examples are
illustrated for our main theorems.
