  Gravitational lensing is one of the most impressive celestial phenomena,
which has interesting behaviors in its strong field limit. Near such limit,
Bozza finds that the deflection angle of light is well-approximated by a
logarithmic term and a constant term. In this way he explicitly derived the
analytic expressions of deflection angles for a few types of black holes. In
this paper, we study the explicit calculation to two new types of metrics in
the strong field limit: (i) the Schwarzschild metric extended with an
additional $r^{-n}(n\geq 3)$ term in the metric function; (ii) the
Reissner-Nordstrom metric extended with an additional $r^{-6}$ term in the
metric function. With such types of metrics, Bozza's original way of choosing
integration variables may lead to technical difficulties in explicitly
expressing the deflection angles, and we use a slightly modified version of
Bozza's method to circumvent the problem.
