Griffiths, who was speaking to Building at the MIPIM property fair last week, described his prediction as a "guestimate" but added: "I am not party to it but I will not be surprised given what has happened if the final cost comes in at half a billion."
Griffiths, who is MP for Edinburgh South, renewed his attack on the civil servants on the project and said the Fraser inquiry would criticise their role.
He said: "It is a classic case of very bad political leadership by the committee in charge of the project. They interfered at every stage and left us with a mess to clear up. I think the staggering level of incompetence of the committee that oversaw it will be exposed by the inquiry, and is being exposed."
Griffiths said the troubled scheme had done the image of the Scottish parliament "no favours at all" but noted: "In a decade we will look at the it as a showcase building we can be proud of."
Griffiths made his comments as the Fraser inquiry into the problems on the project went into its 11th week. RMJM chief executive Brian Stewart broke down in tears last Thursday while describing how he first heard of the illness of Enric Miralles. The Catalan architect died in the summer of 2000 of a brain tumour.
Stewart said such a project "was an impossible thing to deliver" and described his experience on the job as a "nightmare". Speaking about the client he said: "To look at a body of this nature [the Scottish parliament] to procure a building like this is a nightmare. I would never design a parliament building again, even if I was asked. It is an impossible thing to deliver."
John Campbell, the counsel to the inquiry, asked him whether he told officials to be more realistic. Stewart replied: "In 1999 I did. After the election I realised that the pressure was intolerable in relation to the design that was being delivered and the declared budget."
Stewart said one of the problems that he had faced was that the parliament had initially been expected to house 329 people but this figure had grown to almost 1200.
Stewart's evidence came as doubts emerged last weekend that the scheme would be completed by the summer deadline.
A report in Scotland on Sunday quoted Peter Wilson of the Manifesto Foundation for Architecture at Napier University, saying: "I am very sceptical of claims that it will be ready in just four months."
To back up his comments, Wilson pointed to a huge crane in the middle of the building site, as well as unfinished cladding work. He said: "This does not look like a building a few months from completion."
The scheme is due to be completed in August, in time to be officially opened by the Queen in October.
Words of praise: A ‘very clever building,’ says RIBA boss
He said: “Looking down from Carlton Hill it will look an interesting building, although in many ways one might think of it as a strange form of building for the old town of Edinburgh. I think it is a very clever building that does seem to fit in the site in an interesting way.”