The “Month of Psalms NASB Edition Free”iPhone, iPad or iPod Touch application lets you read the psalms in the NASB translation over one month. It is very simple to use with the first page giving you a choice of days 1-31, so you’ll have to double up a day for some months, and even more so in February.
Just tap on the day and you can read through the psalms selected for that day.
Other, more complete bible study applications would also offer this option – but if you are interested in reading just the Psalms in one month then this is a much simpler way to go about it. Also, it is available as a download, and there are no other free alternatives to download the NASB (apart from YouVersion for a limited time).