1、continue doing sth 是继续做刚才没做完的那件事。continue to do sth 是作完一件事继续做另一件事的意思。
试比较：
1、After he finished reading a novel,he continued to play games with his friends.
他读完小说后跟朋友们继续玩游戏.
We hope to continue to have her close support and friendship.
我们希望她能继续大力支持，并能与她维持亲密友谊。
I hope they continue to fight for equal justice after I'm gone
我希望我走了以后他们能继续为司法公正而战。
The commission remains so weak that it will continue to avoid confrontation with governments.
该委员会的力量仍然十分薄弱，所以将继续避免与各国政府发生冲突。
2、After a rest,he continues his reading.
稍事休息后,他继续看书..
The population continues increasing.人口持续增长。
The rain continued falling all afternoon.
这场雨整整一下午都下个不停。
She wanted to continue working until she was 60.
她想要继续工作到 60 岁。
注意：1、continue to do sth和continue doing sth二者虽然都有继续的意思，但继续做的对象是不同的。
2、如果上下文并没有明确是接着做不同的事，还是接着做同一件事，只说接着做，继续做，这两种表达方式就都可以用。
I hope they continue to fight for equal justice after I'm gone...
我希望我走了以后他们能继续为司法公正而战。
Interest rates continue to fall
利率持续下调。
There is no reason why you should not continue with any sport or activity youalready enjoy.
没有理由停下你一直在进行的体育运动或活动。
