I'll be using one of the analog in to monitor a signal. I'll be capturing positive voltage spike (5us spike) around 3v but the I notice that there are also negative spikes (-3v). Would the negative spikes damage the A/D?
Probably destroy the input protection circuits for that pin or the whole chip (via SCR latchup). You defintely should never do this.
I have try to use a diode but the signal is too weak that even the positive spike can't pass through. It may also that the diode I have is not fast enough to respond to a 5 us signal. I'm planning to just directly connect it to the analog input I just want to make sure that it won't damage the A/D.
Then you've put the diode in the wrong place. anode to ground, cathode to the analog input pin. Add a resistor (1k will do) between the source and the analog input. The diode is reversed biased for positive signals and will not affect them at all.
Since the spike is so short you should be thinking of using the on-chip comparator circuit, not the ADC (conversion time 110us as has been mentioned).