[Nightedge]

Could I use towards?

-His becoming her subject of obsession was intrigued by his ignorance __ the existence of iphone.

In dictionaries I find only of/about, but towards sounds OK to me.

[susan53]

No, it must definitely be "of".

towards is mainly used with its meaning of movement in a certain direction, either physical movement (he walked towards me) or metaphorical movement such as change (There has been a change towards shorter but more frequent exams). It does have several other uses and I suspect you are overgeneralising its use to describe behaviour, attitude and certain emotions :

He behaved very badly towards his parents.
I felt no anger towards him, despite what the had done.
She was very hostile towards me.
President Obama claims that his policies have generally been very friendly towards business.
I can't work out what his attitude towards the idea is.

Ignorance has two meanings I = bad behaviour 2 = the state of not knowing something. So in its first meaning it falls into the category I described before (behaviour/attitude) and towards could be used - here's a headline from the University of Montana's website : Ignorance towards minorities sparks diversity iniative. Here ignorance clearly means bad behaviour.

But in your example, ignorance is used with its other meaning - lack of knowledge. And in this case the preposition is always of, about, regarding or some other similar word.

Incidentally the beginning of your sentence is weird - it makes no sense. I can't work out what the subject of "was" is. Only a person can be intrigued by something . You could say eg David was intrigued by her ignorance of etc...

[Nightedge]

Excellent answer. I like the corrections.