This paper investigates the number of switchings and design of switching sequences for controllability of switched linear systems. Two related results are established. One is a new constructive approach to designing switching sequences. The controllable state set of each switching sequence designed via the approach coincides with the controllable sub-space of switched linear systems. The other is a well-estimated value for the minimum number of switchings required for controllability. Each state in the controllable subspace can be steered to origin within this value of switching times.